Despite a promising second-half display from the Light Blues after an evenly played out opening 45 minutes, substitute Adam Idah scored the only goal of the game on the 90 minute mark as the Gers suffered defeat in their final match of the season.
The Gers lined up at the National Stadium with Jack Butland between the posts, behind a backline of captain James Tavernier, Leon Balogun, Ben Davies and Ridvan.
Mohamed Diomande partnered Nico Raskin in the midfield, with Todd Cantwell operating in the number 10 role.
Dujon Sterling and Fabio Silva provided support from the flanks to lone striker Cyriel Dessers.
Celtic looked to get on the front foot as both sides settled into the game in the opening stages. A ball down the side saw Daizen Maeda get the better of James Tavernier, but Leon Balogun did well round on the cover to sweep away any early danger.
The Light Blues started to make moves in the final third themselves after five minutes of the contest. A quick, clever goal kick from Jack Butland was latched onto by his captain, driving forward he did well to find Todd Cantwell on the edge of the area, but his shot was deflected wide in his first effort of the match.
Both sides had more than settled into proceedings beyond the ten-minute mark at Hampden. Clear chances remained at a minimum in the opening stages with a cagey start to the final fixture of the season.
A promising opening was created by the Gers courtesy of some clever play from Nico Raskin and Cantwell. The latter found himself in space and able to drive towards the Celtic backline. He acknowledged Cyriel Dessers to his right but he got the shot wrong before the eventual rebound in the second phase of play was fired over the top.
The Light Blues started growing into the game as yet another shooting chance popped up. Cantwell the provider again, this time finding Fabio Silva to his left who got the beating of Alistair Johnston who initially stumbled, but his shot lacked the desired power as it was claimed by Joe Hart.
At the other end, Rangers had some defending to do as Celtic probed around the edge of the area. An initial pass across the box from Greg Taylor was met by the head of Matt O’Reilly, his knockdown was met well by Reo Hatate but Ben Davies did well to divert any danger with his head as the chance was cleared.
The best chance of the contest arrived just short of the 25 minute mark. A wide delivery from Cantwell was fired low into the box, it fell to the feet of Dessers who worked the angle for the shot but was bombarded by several bodies with O’Reilly making the block before he was closed down for any rebound, with Clement’s men looking a threat when they got the chance to move forward.
Celtic came the other way minutes later after a driving run from defence from Johnston. Carrying the ball after combining with Calum McGregor he found his way into the Rangers box with the initial shot blocked before his second effort had to be turned round the post by Butland after coming through a crowd of bodies.
Several stoppages in play saw the flow of the game brought to a halt as the match approached the interval, with Rangers shading the better of the openings but neither goalkeeper having really been tested inside the opening 40 minutes.
A James Tavernier corner that had to be tipped over the top of his own crossbar was the closest either side came in the closing seconds as they went into the interval locked level at 0-0.
Rangers introduced Abdallah Sima at the break as they looked for further energy in their frontline at the start of the second half in the sunshine at Hampden.
The end of the first half theme continued into the beginning of the second. Rangers looked at their most threatening in changeovers inside their own half but were unable to create any meaningful counters to sustain further attacks.
An opportunity broke for Ridvan as he did well to intercept a pass out from the Celtic backline. The Turkish international won the ball high and with space in front of him, but his shot lacked power as it rolled into the hands of Hart on the deck.
Celtic had an opportunity of their own at the other end. A pass wide was latched onto by James Forrest who chopped inside, but his shot hit a combination of Rangers two centre-backs before landing in the hands of Butland.
Rangers thought they had taken the lead through Abdallah Sima after getting on the end of a James Tavernier corner. The forward met the ball at the back post as he bundled it over the line with his knee after it came through a crowd of bodies. However, an on field VAR decision saw referee Nick Walsh disallow the goal after deeming Nico Raskin to have pushed goalkeeper Joe Hart in the area before it was turned into the net.
It was the Light Blues who looked the more likely but it still remained goalless at the 70 minute mark in Mount Florida. Both sides turned to their substitutes on two further occasions as they looked to inject further life into the cup final and find a breakthrough.
Rabbi Matondo got involved straight away in the contest as he settled right into proceedings. Carrying the ball over 30 yards he looked to drive the Gers forward as he picked out Dujon Sterling to his right, but the wide man saw his shot blocked before the following corner came to no avail.
A Ridvan cross was met by the head of Sima at the back post after a quick throw-in, but his effort lacked the desired power on the stretch as the Gers looked to up the anti-inside the final ten minutes of normal time.
A real counter-attack opportunity for the Gers was wasted at the end with a great opening eventually falling to Sima. Substitute Scott Wright drove forward through midfield before Raskin picked up the loose ball, he delayed the pass before playing in the frontman to his right, but he got his effort wrong as it was saved comfortably by Hart.
Just as the game headed for stoppage time and for all of Rangers’ good second-half play, it was Celtic who made the breakthrough. Paulo Bernardo drove from deep as he made his way towards the edge of the area, he tried his luck from the edge of the area with the shot parried initially by Butland before Adam Idah was on hand to tap home the rebound.
Despite the eight additional minutes of stoppage time, Rangers were unable to create any further openings to find a way back into the game as they fell to defeat in their final match of the 2023/24 season.
CELTIC: Hart, Johnston, Carter-Vickers, Scales, Taylor, McGregor, O’Riley, Hatate (Bernardo 78), Forrest (Kuhn 70), Kyogo (Idah 61), Maeda
SUBS: Bain, Palma, Nawrocki, Iwata, Ralston, Welsh
RANGERS: Butland, Tavernier, Balogun, Davies, Ridvan, Raskin (Lundstram 90+4), Diomande, Cantwell (Wright 73), Sterling (McCausland 80), Silva (Matondo 73), Dessers (Sima 45)
SUBS: McCrorie, Lundstram, Jack, Dowell, McKinnon
REFEREE: Nick Walsh