The midfielder moved last week from Guingamp for a fee reportedly in the region of 7.5million euros (£6.5m), signing a five-year contract.
Imbula is only 20 years old and has never played in the top flight but Marseille sporting director Jose Anigo said: "He is ready for OM.
"He has the technical potential and I was able to judge his character during our discussions."
Baup added: "I have no doubts over him.
"He plays an important part in the game, with his ease on the ball and ability to get forward and support the front line.
"He certainly has room to progress but he is already part of our plans."
Imbula was also courted by big-spending Paris St Germain but was drawn to Marseille by their greater stability and the passion of their crowd.
He said: "I like this club. Marseille are a club with fervour, with supporters who love the club.
"At Paris there are signings all the time, every week, every month. That does not interest me, I prefer a stable club with values."
OM, for their part, have signed Dimitri Payet from Lille and Benjamin Mendy from Le Havre as well as Imbula, and have been linked with out-of-favour Lyon forward Bafetimbi Gomis, Lille's Florian Thauvin, PSG midfielder Adrien Rabiot and Rennes right-back Dimitri Foulquier.
President Vincent Labrune said: "It is likely that we will have a new arrival here between now and the end of the window."
Whether that arrival will be Joey Barton, following his loan spell from QPR last month, is in the hands of the English club.
"We made an offer in May which has not had a response," Labrune added. "The player belongs to QPR, they will decide."