In return, the Penguins gave up a conditional seventh-round pick in this year's draft. The pick turns into a sixth-rounder if Pittsburgh reaches the second round of the Stanley Cup playoffs and Kovalev appears in at least 50 percent of the first-round games.
The trade is Pittsburgh's second in four days, as the team attempts to shore up a banged-up roster that is missing 12 regulars. Earlier this week, they picked up James Neal and defenseman Matt Niskanen from the Dallas Stars in exchange for defenseman Alex Goligoski.
Kovalev, 38, had to waive a no-trade clause to close the deal. He is expected to join the Penguins in time for their Friday game in Carolina.
Kovalev, who won a Stanley Cup with the New York Rangers in 1994, is in the final year of a two-year deal with the Senators that paid him $5 million annually.
He has been a major disappointment in Ottawa, with 14 goals and 13 assists for 27 points in 54 games.
A 17-year veteran, Kovalev has 426 goals and 591 assists in 1,282 career games entering Thursday. He played for the Penguins from 1998 through the 2002-03 season before being traded to Montreal.
Kovalev was a two-time All-Star selection during his time in Pittsburgh and had a career-best 95 points (44 goals, 51 assists) in 2000-01.
The trade for Kovalev was announced shortly after coach Dan Bylsma revealed that defenseman Brooks Orpik will miss between four
and six weeks with a broken finger on his right hand.
Orpik was hurt when he was struck by Patrick Marleau's shot late in the first
period of a 3-2 overtime loss to San Jose a day earlier.
Defenseman Paul Martin has a chance to return Friday, as he was
listed as day to day after missing two games with an upper body
The rash of injuries have sent the Penguins in a tailspin,
though they remain in playoff contention, sitting in fourth in the
They're 2-5-2 in their past nine games and are struggling
particularly on offense, which has produced five goals during the
team's 0-1-2 skid.
Pierre LeBrun covers the NHL for ESPN.com. Information from The Associated Press was used in this report.