NFL Network first reported the news of Church's expected deal.
Church's addition likely signals the Jaguars will not re-sign safety Johnathan Cyprien, who also is a free agent.
Church, who joined the Dallas Cowboys as an undrafted free agent in 2010, became a starter in 2012 -- only to suffer a torn Achilles in the third game. Despite the injury, the Cowboys rewarded him with a four-year deal, and Church started every game he played from 2013-16, missing just five games.
He missed four games last season because of a broken forearm, yet he still managed to finish third on the team with 85 tackles. He also led the Cowboys with two interceptions and was credited with two tackles for loss, four pass deflections and one forced fumble.
During Church's midseason absence, the Cowboys did not record a takeaway. Upon his return, the Cowboys recorded five interceptions and five fumble recoveries over the final five games.
Church, who turned 29 in February, served as a Cowboys defensive captain the past two seasons. For his career, he has five interceptions, six quarterback pressures, seven forced fumbles and three fumble recoveries.
ESPN's Todd Archer and Michael DiRocco contributed to this report.