Rangers were drifting away following a run of poor performances and results, which resulted in Beale’s sacking earlier in the season.
Clement was brought in as his replacement but not much was being expected in terms of an immediate impact as many felt Rangers wasted money on average players in the last summer transfer window.
However, the Belgian has managed to take Rangers to the last 16 of the Europa League as group winners and they also won the Scottish League Cup on Sunday at Hampden Park.
Rangers are within reach of Celtic at the summit of the Scottish Premiership and Thompson conceded that Clement’s performance has been nothing short of incredible.
He stressed that Rangers were being written off when Beale got sacked as they were on the floor and there were several question marks around the quality of the squad.
The former Rangers star also stressed that Clement will not kick his heels as he will demand more from the players going forward this season.
Thompson said on BBC Radio Scotland: “Yes, they have [bought into Philippe Clement].
“Today was absolutely massive but the success he has had in such a short space of time has been incredible.
“You go back to when Michael Beale left the club, Rangers were on the floor.
“There were so many questions about recruitment, about them going another season without a trophy, without any real hope for the season ahead.
“He has completely turned that around and in a short space he has taken Rangers into the Europa League final last 16, won his first trophy as Rangers manager but it won’t be enough for him.”
While Clement plots Rangers’ next move, Beale has been strongly linked with taking over as the new manager of Championship side Sunderland.