The Netherlands international is poised to complete a switch to Old Trafford on Monday after current club Ajax accepted a bid of £13.8 million from United.
Blind is quoted by The Telegraph as saying: "I got a call on Friday night [telling me] that the clubs had agreed a deal.
"I was with my girlfriend and we went to my parents to drink a glass of wine.
"I am enormously proud to be at one of the biggest clubs in the world. Everything has happened so suddenly.
"What exactly has gone off in the background, only my agent and my dad know, but it was a very exciting and tense time."
It is unclear which position the left-sided Blind is likely to adopt at United, where he will link up with former national team coach Louis van Gaal.
The 24-year-old was utilised in a variety of positions by Van Gaal at the recent World Cup in Brazil.
Blind added: "Did I speak with Louis van Gaal in the last few days about the role I am going to play at United? We did have some informal contact, but the conversations which took place stay between him and me.
"I just want to be part of the team, in whatever role that is going to be, in defence or in midfield."
