Ambrose spent the second half of the season on loan from Celtic, helping Hibs lift the Championship trophy, and has agreed to make the move permanent after ending his five-year spell in Glasgow.
The 28-year old defender follows St Johnstone midfielder Danny Swanson and Dundee United forward Simon Murray in committing to Hibs when their current deals formally expire.
It was Hibernian manager Lennon who brought Ambrose to Scottish football when he signed him for Celtic in 2012.
The Nigeria international, who has 51 caps for his country, won four league titles, a Scottish Cup and a League Cup in his time at Celtic Park.
