Minnesota confirmed the signing but not the contract terms.
Kline became available five days ago when the Titans released him one season into his four-year deal. He was a three-year starter for Tennessee.
Kline, 29, entered the league undrafted in 2013 out of Kent State. He spent the first three seasons of his career with the New England Patriots.
The Vikings had just $1.85 million in cap space before signing Kline, according to Over The Cap.