Olid, 40, led Hearts to their first Scottish Women’s Premier League title last season.
Man Utd director of women’s football Matt Johnson said: "Eva is an outstanding coach with an incredible determination to succeed.
"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. We are delighted that she will now bring those qualities to Manchester United.
”Eva is the perfect coach to lead us into an exciting new era. She shares our commitment to developing exciting homegrown and young players, a tradition deeply embedded in our club’s history and culture, as well as improving established senior internationals, both of which form an integral part of our vision for long-term, sustainable success."
Olid spent five years at Hearts and took them from the second tier of Scottish football to a first Premier League title.
She said: "The opportunity to become head coach of Manchester United Women is a dream come true.
"The club has outstanding infrastructure and everything we need to achieve our ambitions. We have an excellent training facility, an academy that is already producing players capable of performing in a competitive first team, and an exceptional group of support staff.
"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. I cannot wait to begin preparing a team that will make our incredible supporters proud."
Olid has signed a contract until June 2028, with the option to extend for a further year.