The Sounders announced the moves Thursday. Barrett was selected in stage two of the MLS re-entry draft in December.
Barrett spent last season with New England and had two goals and two assists in 19 games. He previously played for Chicago, Toronto and Los Angeles.
Kovar and Okoli are the second and third homegrown players signed by the Sounders in the past two seasons. Kovar, a midfielder from Seattle, was the Pac-12 freshman of the year in 2012 playing for Stanford. Okoli, a forward, grew up in Federal Way and played at Wake Forrest. He was a first-team all-ACC selection in 2013.