The deal is for $10 million, according to MLB.com, which first reported the two sides were close.
The Cubs were in the market for a first baseman because they traded Derrek Lee to the Braves in August and lost Xavier Nady to free agency. Natural outfielder Tyler Colvin was their top in-house option at first before bringing in Pena.
An All-Star in 2009, Pena's numbers dropped with the Rays last season. The power-hitting lefty hit a career-low .196 with 28 home runs, his lowest total since coming to Tampa Bay in 2007. With a one-year deal, Pena gets the chance to bounce back and command more money next year if he performs well with the Cubs.
Pena is set to join a Cubs lineup that includes fellow established power hitters Aramis Ramirez and Alfonso Soriano as well as up-and-comers Starlin Castro and Colvin.
The signing would allow Colvin, a former first-round pick who showed promise hitting 20 homers in platoon duty last season, to stick in the outfield. It could also lead to the departure of Kosuke Fukudome, whom the Cubs have reportedly been looking to trade.