The 23-year-old is closing in on a move to Tynecastle Park when his Livingston contract expires this summer. Hearts want him on a long-term deal and he is ready to take the next step in his career after several rounds of talks with the club.
Hibs had been credited with an interest in Halkett, who earlier this week admitted it was a "compliment" to be linked with Hearts. He is now set to swap West Lothian for Gorgie after three and a half years with Livingston.
Halkett is a product of the Rangers youth academy but left Glasgow in January 2016 seeking regular first-team football. He quickly became a key player and helped Livingston record back-to-back promotions, taking them from League One into the Premiership in successive seasons.
He was appointed captain last season but, after more than 100 games for the club, is set for pastures new at Tynecastle this summer.