The 27-year-old was unveiled to the media on Wednesday after talks with United progressed last week.
Barcelona hold an option to make the move permanent next summer at a reported fee of €30 million (£26m).
Rashford's wages will be covered for the duration of the loan and it is thought he has taken a 25 per cent pay cut to join the Spanish giants.
The England forward, who will wear the number 14 shirt, trained with his new teammates for the first time on Tuesday as Barcelona prepare for a pre-season tour of Asia.
He will also become the first Englishman to play for Barcelona since Gary Lineker in the late 1980s.
"I'm very excited," Rashford told Barcelona media. "It is a club where people's dreams come true, they win big prizes.
"What the club stands for means a lot for me. I feel like I am at home and a big factor in my choice to come here because it is a family place and a good place for good players to showcase their skills."
Barcelona has long been a preferred destination for Rashford, who will be embarking on a second straight loan spell.
He spent the second half of last season on loan at Aston Villa after dropping down the pecking order at United under Ruben Amorim.
Rashford last played for United in December and has scored 138 goals in 426 matches since making his debut in 2016.
A move away from Old Trafford seemed a given this summer with his number 10 shirt handed to new signing Matheus Cunha.
"I want to say thank you (to the fans) for the warm welcome," Rashford added. "It is a different environment and I am enjoying every minute. It feels like home.
"We as players appreciate all the support, but for a new player the first time in the stadium together is going to be a special moment. I am looking forward to seeing you all and appreciate all the support."
However, Barcelona are currently unable to register Rashford to compete in La Liga, although he is able to train and play in non-competitive games.
La Liga's financial rules state clubs can only spend as much as they earn, meaning Barça must find other revenue streams or make player sales to fit in their new signings.
Barcelona's first pre-season fixture is against Japanese side Vissel Kobe on Sunday.