The club declined to offer a 2016 contract to Alvarez by the midnight deadline Wednesday, making him one of 43 players to become a free agent.
A former first-round pick, Alvarez, 28, led Pittsburgh with 27 homers in 2015 but struggled defensively after making the transition from third base to first. Alvarez's 23 errors led the team.
Alvarez was an important part of Pittsburgh's rise to contention. He was an All-Star in 2013, when his 36 homers tied for the National League lead and the Pirates made the postseason for the first time in 21 years. His defense at third eroded in 2014, and he eventually lost the starting job to Josh Harrison.
The club moved Alvarez over to first base full time in spring training this year, but he had difficulty adjusting to the position and was used in a platoon during the second half of the season as the Pirates earned a wild-card berth for the third consecutive year.
"Pedro Alvarez grew up as a Pirate, and he and his wife, Keli, were active members of our organization and our community for the seven seasons that Pedro was with us," president Frank Coonelly said in a statement. "Pedro also made major contributions to the success that we have had over the last several years. We thank him for his contributions and wish he, Keli and his young daughter all the best as Pedro continues his baseball career."
Pittsburgh also declined to offer a 2016 contract to reserve outfielder Jaff Decker. The Pirates did make offers to the remaining players on the 40-man roster who were up for renewal, including All-Star closer Mark Melancon and second baseman Neil Walker, both of whom are entering their final year of arbitration and expected to command a sizable bump in salary.