The turbine manufacturer said the board had decided that a new face was needed at the helm of the company during this "transitionary stage" as Vestas starts to turn around its fortunes following recent difficulties.
"The company is now entering a new phase, where we want to realise our growth potential, and I am confident that Mr Runevad has the right experience to lead the company," said Vestas chairman Bert Nordberg, also a former Ericsson executive.
Engel has been with Vestas since 2005, but has proved a controversial figure in recent years as the company moved to make deep cuts and close a number of factories. He has also been embroiled in a number of legal cases and was voted last in a survey of top business leaders in Denmark earlier this year.
The news came as the company released its second quarter results, which, while showing that the company is turning its fortunes around, were below analysts' expectations. Despite this, shares in the firm lept 5% on Wednesday morning following the news of Engel's departure.
"This is a natural and expected transition. Having completed rigorous restructuring over the past 18 months, facing legal challenges, and criticism from disgruntled stakeholders means the focus has been on Engel rather than on the positives that Vestas has gained from the restructuring and developing a healthy order book," said industry analyst Aris Karcanias of Navigant's BTM.
Commenting on the appointment of Anders Runevad, he added: "It's good to have someone fresh, and particularly someone from the telecoms industry, which has been through the same boom and bust that wind has."
Senior vice president Morten Albaek said: "The change has nothing to do with the law suits the company is involved in, it is just felt that Runevad had more key competencies than Engel."
"He has a strong engineering background, which will allow him a more hands-on approach, while he has also worked across a number of regions."
Runevad joined Ericsson as a design engineer in 1984. Albaek said this will prove useful, particularly considering that the telecoms industry "has a lot in common with wind as they both involve large infrastructure projects".
Runevad also has a wealth of experience in the booming Latin American market, where Vestas has failed to make the same kind of headway as competitors such as GE.
He said: "I am delighted to be joining Vestas and look forward to leading the company in its next phase of development. I believe that my career has equipped me with the right tools to take on this task."
Runevad will take over as group president and CEO on 1 September. Vestas chief financial officer Marika Fredriksson will hold the reins in the interim.