Youssouf Mulumbu says he has joined an “amazing” club after moving to Celtic.
The experienced former West Brom and Norwich midfielder, 31, was a free agent after leaving Kilmarnock at the end of last season.
The Scottish champions have also signed Leicester City defender Filip Benkovic, 21, on a season-long loan.
However, striker Moussa Dembele has left Celtic for Lyon in a £19.7m deal, signing a five-year contract, the French club have said.
Mulumbu’s only goal during his 20 games at Kilmarnock was in a 1-0 win against Celtic but it is his ball-winning qualities that appealed to Rodgers.
Rodgers said on Thursday that the Scottish champions “were always on the lookout for a really aggressive number eight to play midfield”.
Mulumbu told the Celtic website: “The first goal for me is to show to the manager that I’m ready. Anytime he needs me I will respond on the pitch.
“We need to do well in the Europa League, retain all the domestic trophies and continue winning the Glasgow derbies. It’s amazing to be part of that.”
Benkovic joined Premier League Leicester from Dinamo Zagreb earlier this month for a reported £13m.
Rodgers described him as a “highly-rated young centre-half, big presence in both boxes, can play.”
And Benkovic said: “This all happened so fast but I’m delighted that it finished here as this is a very big club with a big history.”
Meanwhile, Celtic have sent 18-year-old striker Jack Aitchison on loan to third-tier Dumbarton until January.
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