The Jets also re-signed backup defensive lineman Leger Douzable to a one-year deal Wednesday.
Giacomini missed seven games with a knee injury last season for Seattle, but was back in time for the Seahawks' run to their Super Bowl title against Denver. The 6-foot-7, 318-pound Giacomini will replace Howard, who signed with Oakland as a free agent after starting every game the last two seasons. Giacomini was a fifth-round pick in 2008 of Green Bay, where he spent three seasons before spending the last three with Seattle.
Douzable signed with New York as a free agent last offseason and had 20 tackles and a career-high 1 1/2 sacks.