The move comes two days after former manager Marc Skinner left the club by mutual agreement, ending a five-year spell weeks before the start of the new season.
The 40-year-old Olid arrives after leaving Scottish side Heart of Midlothian in May after almost five years in charge.
She oversaw the most successful period in the club's history, guiding Hearts from the second tier to their first Scottish Women's Premier League title last season.
The Spaniard's achievements earned her both the SWPL Manager of the Season award and the PFA Scotland SWPL Manager of the Year honour.
"The opportunity to become head coach of Manchester United Women is a dream come true," Olid said in a club statement.
"There is already so much talent within our squad and I am excited to work with the players to support them to fulfil their immense potential.
"I am joining Manchester United at a really exciting time. There is a clear alignment in our shared vision for long-term success."
United, who finished fourth in the WSL last season, said Olid had signed a three-year deal with an option for a further year.
"Eva is an outstanding coach with an incredible determination to succeed," United's women's football director Matt Johnson said.
"Her remarkable achievements at Heart of Midlothian showcased her ability to maximise the potential of individual players whilst also implementing an exciting style of football."
Olid's first competitive match in charge will be at London City Lionesses for the WSL season opener on September 4.