He has been coach of the Netherlands since 2012, his second spell with the national team following a stint from 2000-02.
"Everyone is very excited about this new phase in the club's history," United vice-chairman Ed Woodward said. "His track record of success in winning leagues and cups across Europe throughout his career makes him the perfect choice for us.
"People know him as a larger-than-life character but I have also been extremely impressed by his intelligence, thoughtful approach to the role and his diligence."
He can be spiky and provocative with journalists and hardly lacks in self-belief, a trait which can often spill over to make him appear arrogant. But after the failed tenure of Moyes, United needed a manager who commanded respect and had a strong track record.
His job won't be easy. While United has regressed since landing its record-extending 20th English championship last year, rival Liverpool has improved greatly under Brendan Rodgers and finished second in the Premier League this season. Chelsea, Manchester City and Arsenal are established members of the top group and showing no signs of being on the slide.
The appointment of Giggs as Van Gaal's No. 2 will satisfy those eager for some continuity at the club following the trophy-filled era of Ferguson.
The 40-year-old Giggs published an open letter on United's website an hour after Van Gaal's appointment, praising the Dutchman's qualities and revealing his decision to end his playing days.
"For me, today is new chapter filled with many emotions — immense pride, sadness, but most of all, excitement towards the future," Giggs said. "United fans I hope will share and echo my belief that the club, the management and owners, are doing everything they can to return this great club to where it belongs, and I hope to be there every step of the way."