The 23-year-old, who has skippered the Jambos back to the Scottish Premiership at the first time of asking, has told the club that he is seeking a new challenge.
His last act in a Hearts shirt will be to lift the Championship trophy on the final day of the season at Tynecastle and Neilson told Hearts News that the centre-half will leave the club with everyone’s best wishes.
He said: “Danny’s decided he wants a new challenge and, as I’ve said previously, I’ll never stand in the way of any player who wants to move on, so he goes with our blessing and our thanks.
“He’s been an outstanding servant to this club and has played a vital part in its revival this season.
“Danny’s probably seen it all in the two and a half years that he’s been here and probably had good cause to leave sooner if he had wished to do so.”
Scotland cap Wilson joined Hearts on loan in January 2013 before signing a permanent deal that summer. He skippered the side in their fight to stay in the top flight after the club were plunged into administration.
He has made 84 appearances in a maroon shirt, scoring 10 goals, including five this season.
Neilson added: “He took a pay cut during the bad times and was instrumental in helping to keep spirits up when things looked bleak; buying season tickets and donating them to club charity Big Hearts, and donating several raffle prizes for club events and then buying them back.
“He had options to go at the start of this season but he stayed because he wanted to see the job through and get us back to the top flight so for that I can’t thank him enough.
“We’ll miss him on and off the park and he’s been a great captain but that’s football; players join and players leave and we’re no different here at Hearts.
“We’ll continue to work hard to assemble a squad that can challenge for a top-half spot in the Premiership.”