The talented midfielder is the Imps' first addition of the summer following his release by Notts County.
Butcher, 28, has agreed a two-year deal at Lincoln and is aiming to make the most of his third spell at the club.
He told the Lincolnshire Echo: "I do have unfinished business here and that was certainly one of the reasons why I returned.
"Losing the two play-off finals are certainly the biggest regrets I have ever had in football.
"Even now when I think about those disappointments they still hurt despite all the time that has passed since then."