General manager Reggie McKenzie announced the deal with the eight-year veteran on Friday.
Kluwe played in 127 games for the Minnesota Vikings with a 44.4 yard career average. He ranks second all-time in Minnesota history with a 37.3 net average.
Lechler left Oakland as a free agent this offseason after spending the past 13 years with the Raiders. Oakland released punter Bobby Cowan but still has Marquette King on the roster. King impressed the team in training camp last summer and spent the year on injured reserve.