The Netherlands international is poised to complete a switch to Old Trafford on Monday after current club Ajax accepted a bid of €17 million from United.
"I got a call on Friday night telling me that the clubs had agreed a deal," Blind told reporters. "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 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 the coach at the 2014 World Cup in Brazil.
"Van Gaal and I did have some informal contact before the move, but the conversations which took place stay between him and me," he added.
"I just want to be part of the team, in whatever role that is going to be, in defence or in midfield."