ESPN revealed in May that Jurado, who has been at Barca for almost a decade, had turned down several offers to stay at Camp Nou in favour of a switch to the Premier League club.
The right-back's non-professional terms expired on June 30 but he has been eligible for a professional contract since he turned 16 in April.
Barca offered him a three-year deal that would have been worth €100,000 annually by the end of the contract, with a €200,000 bonus included if he made his debut for the B team.
However, Jurado turned down the chance to stay with the club and will instead try his luck in England with United, who will only have to pay development rights as he is out of contract.
"It's never easy to leave the club that has given you everything," Jurado wrote on Instagram on Monday. "Barcelona has been my second home, my second family, where I have grown as a player and also as a person. Now it is time to say goodbye but not before thanking every one of the people that have helped me since I joined in 2011.
"I've been lucky enough to share my passion with a fantastic generation of players. We started as kids that just wanted to chase the ball and I bid farewell, nine years later, able to call them my friends. We have had tremendous luck with the coaches we have had and that have developed us and helped us to keep fulfilling our dreams.
"Everything has a beginning and an end. My end, after reflecting with my family, has arrived. I leave behind unforgettable memories that I will always carry with me."
A source told ESPN that Barca are disappointed to lose the defender and are especially upset with the way his agent, Carlos Lacueva, the son of one of the club's former directors, handled the situation.
Jurado becomes the latest in a string of players to leave La Masia before reaching the first team. Barca lost both Eric Garcia and Adria Bernabe to Manchester City in recent years, while other players have left for Borussia Dortmund, Monaco and Juventus.
However, the club remain committed to their academy and Pablo Paez -- better known as Gavi -- and Ilias Akhomach, who were part of the same under-16 side as Jurado this season, will sign professional deals.
Meanwhile, United States youth international Konrad de la Fuente became the latest player from the U19 team to sign a new deal and be promoted to the B team over the weekend.
De la Fuente, 18, has signed new terms until 2022 with an option for two more years. His contract features a €50 million buy-out clause, which will be increased to €100m if he reaches the first team.