Albion announced in the final hour before the summer window closed at 11pm that Benin international Sessegnon had joined them from Sunderland on a three-year contract.
The fee was undisclosed, although the Baggies said it had broken their transfer record, surpassing what they agreed with Reading for Shane Long in August 2011.
Everton later confirmed Nigerian frontman Anichebe had left them to sign for West Brom for a fee which could rise to B£6million.
The Toffees' statement also said they had tied up a season-long loan deal for Chelsea striker Romelu Lukaku, who West Brom had reportedly been looking at re-signing themselves.
Meanwhile, Odemwingie wrote on Twitter that he was signing for Cardiff.
The Nigerian had been on the periphery at Albion since he failed to secure a move to QPR on transfer deadline day in January, despite turning up at Loftus Road in his car.
Earlier on Monday, West Brom had confirmed two other signings in Marseille midfielder Morgan Amalfitano, recruited on loan until the end of the season, and Northern Ireland international goalkeeper Lee Camp, previously free agent, on a rolling contract until January.
Sessegnon, 29, arrived in English football in January 2011 when Sunderland signed him from Paris St Germain.
He went on to make 97 appearances for the Black Cats, scoring 18 goals.
Anichebe is an Everton academy graduate. The 25-year-old netted 26 times for the Toffees in a total of 168 appearances.
Amalfitano, 28, had been with Marseille since the summer of 2011.
He has one international cap for France and has also played for Lorient and Sedan.
Camp has been signed as cover for Albion's injured England stopper Ben Foster.
The 29-year-old has spent time at Derby, Burton, QPR, Norwich and Nottingham Forest.
As for Long, it seems he nearly left West Brom on Monday.
Press Association Sport understands the striker was given permission to depart the Republic of Ireland's training camp to discuss the prospect of a transfer from Albion to Hull.
The 26-year-old was reportedly at the Tigers' training ground when it emerged Baggies boss Steve Clarke had pulled the plug on the deal.