The trade was announced on Sunday.
Lueke made the Mariners opening-day roster last season, but was optioned to Triple-A Tacoma in April after allowing 12 runs over 6 1-3 innings in eight appearances. He rejoined the Mariners in July and in 25 games overall had a 1-1 record with a 6.06 ERA.
"Josh has the stuff to get hitters out in the American League East and began to show that during the second half of last season," Rays executive vice president of baseball operations Andrew Friedman said. "We believe he can be an important part of our success here for many years."
Jaso batted .224 in 2011 with five home runs and 27 RBI in 89 games.