Cole's contract was to expire at the end of the season but the England international has agreed a new deal, manager Rafa Benitez said on Sunday after a 2-1 home victory against Arsenal.
"I'm really pleased. The paperwork has to be done but the agreement is there," Benitez told the club's website.
"We are happy and he is happy"
Lampard is revered at Chelsea and now stands only seven goals behind the club's all-time record scorer Bobby Tambling.
Benitez praised Lampard's contribution since he returned from injury but offered no new insight on the players' future.
"I can understand that Frank, from day one, has been doing a great job. He is under contract, his commitment is there and I'm really pleased with him," Benitez said.
"Every player here has to compete for his position. That's good for the team, and also for me as a manager because I can make decisions."
"Every game you win, especially when you show quality and character, is always positive for the players ahead of the next game," he said.
"Winning against a top side is always important. When you are in the top four, and you want to be sure of staying in the top four, Arsenal are one of the biggest rivals."
While it was a good day for Chelsea, captain John Terry's failure to make the starting line-up was a surprise.
"Terry has to play, but you cannot play him in this type of game as he will have to play high, and that's more difficult if he's not fit," Benitez said.
