West Brom have sacked Nicolas Anelka citing "gross misconduct" after the striker claimed on Twitter he had quit the club.
Mauricio Pochettino expects to be at Southampton next season and is looking forward to working with chairman Ralph Krueger.
The former United captain, who made 707 appearances for the club, was replaced as assistant manager by Simon Donnelly when Jackie McNamara was brought in following the exit of Peter Houston. Darren Jackson also joined the coaching staff.
A club statement read: "With the installation of the new management team now complete, Dundee United confirm that an amicable agreement has been reached with former assistant manager Paul Hegarty.
"Paul, who also served Dundee United as player, club captain, coach and manager, leaves with the best wishes and grateful thanks for his many years of exemplary service on behalf of the club and will always be welcome at Tannadice Park."