The announcement regarding Mears' three-year deal with the Clarets is expected in the next day or so, according to his agent Willie McKay.
"Tyrone has agreed personal terms and passed a medical at Burnley," McKay told skysports.com.
"He has agreed a three-year deal and he should be unveiled in the next 24 hours.
"Tyrone really enjoyed his time at Marseille, but he could not turn down the chance to return to England with Burnley.
"He is really excited by the move and is looking forward to helping Burnley in their first season in the Premier League."
Mears spent last season on loan with French Ligue 1 club Marseille and has previously had spells with West Ham and Preston.