After spending four years at Seaview as a player, Baxter took over as manager in 2005 and helped them gain promotion back to the Irish Premiership in his second season in charge.
He then guided the Crues to their first Irish Cup success in 41 years when they beat Cliftonville 1-0 in the 2009 final at Windsor Park.
Baxter brought back-to-back Gibson Cups to Seaview in the 2014-15 and 2015-16 seasons, before lifting the league title again in the 2017-18 campaign.
Three more Irish Cup triumphs followed in 2019, 2022 and 2023.
“The manager is the one who has to motivate, and at times he doesn’t always have someone to motivate him,” O’Neill added.
“So to have that enthusiasm for the game and that dedication to one club, and to have the periods of success that he’s had and those difficult periods, I think that is testament to Stephen’s character.
“They are big shoes to fill, but what has happened in Crusaders in recent years, Stephen has played a huge part in that.”