The swap of relievers followed the decision by left-handed reliever Scott Eyre to leave the Giants and sign with the Chicago Cubs.
"The first thing that comes to mind is we might of dodged a bullet of losing Scott," Giants general manager Brian Sabean said. "This guy has got quite a track record."
Kline, who is 33, pitched under Giants manager Felipe Alou with the Montreal Expos. He was 2-4 with a 4.28 ERA last season -- with a 2.83 ERA after the All-Star break. He has a 29-34 career record with 36 saves and a 3.40 ERA.
"I think a return to the National League will be what he needs, although he had a great second half," Sabean said. "So we consider ourselves fortunate."
Sabean said Kline is like Eyre in that he's durable and wants the ball all the time. Of Kline's 656 major-league appearances, 569 have come in the National League, and he has appeared in at least 67 games in each of the last eight seasons.
Hawkins, who turns 33 on Dec. 21, was acquired by the Giants on May 28 from the Chicago Cubs for right-handers Jerome Williams and David Aardsma. Hawkins was a combined 2-8 with six saves and a 3.83 ERA, but became expendable for the Giants when they signed right-hander Tim Worrell to a $4 million, two-year contract last week.