The Senegal international will vie for a role up front at Stamford Bridge next season with the likes of Fernando Torres, Andre Schurrle and Romelu Lukaku.
Chelsea have also seen a bid rejected for Manchester United forward Wayne Rooney.
"I will stay," he said.
"I think we need competition and we welcome the best players in this club.
"More competition is going to make me better anyway. All players want to play, not only centre forwards.
"We will all work in the same direction, for the club, to try and win the games."
Ba was on the scoresheet during Chelsea's 8-1 win over Indonesia All Stars on Thursday.
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