ESPN first reported the deal.
The injury-prone Eifert played just two games in 2017 before undergoing another back surgery. He has appeared in more than eight games just twice in his five-year career in Cincinnati.
When he's on the field, the 6-foot-6 tight end is a red-zone maven, catching 13 TDs in 2015.
A slew of injuries, however, cast his future in doubt. ESPN reported last month NFL teams were notified that Eifert was cleared by Dr. Robert Watkins to participate in organized team activities this spring and play in 2018.
Last year's surgery was Eifert's third on his troublesome back. He was burdened with a knee issue for a portion of the 2016 season, and he dealt with an ankle injury at the outset of that campaign. For his career, Eifert has missed more regular-season games (41) than he's participated in (39).
Eifert, ranked No. 37 on NFL.com's Top 101 Free Agents of 2018, was pegged as one of the big X-factors hitting the open market.
If healthy, Eifert provides Andy Dalton a proven touchdown target. That's a big if at this stage. With a one-year prove-it deal in place, the big tight end will try to recapture his 2013 form before hitting free agency again next year hoping to cash in.