The Titans announced the deal Sunday with no terms immediately available.
They agreed to terms on a five-year, $15 million deal with punter Brett Kern on Saturday night. Brinkley has been Kern's snapper the past three seasons after signing as an undrafted free agent in 2012.
Last season, Brinkley ranked third on the team with a career-high 10 special teams tackles, and he helped Kern set a team record for net punting average in a season.
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