The Englishman was at Tynecastle Park on Wednesday night to watch Hearts beat Hibs 2-1 and has agreed a deal to continue his career in Scotland next season.
He is out of contract at Luton having helped them gain promotion to England’s League One. Hearts moved quickly to make the 26-year-old manager Craig Levein’s fourth capture ahead of the new campaign.
Steven MacLean, Uche Ikpeazu and Bobby Burns have all signed already, with Jake Mulraney expected to follow suit.
Lee is the son of former Newcastle United and England midfielder Rob Lee. He is known as a cultured passer of the ball and was previously on the books at West Ham United, Birmingham City and Barnet.