Krack has followed a similar career path to McLaren team boss Andreas Seidl, having worked with BMW in F1 early in his career before gaining experience in other categories.
He joined Sauber in 2001 and rose to the position of chief engineer in the works BMW era, and thus spent some time working with current Aston river Sebastian Vettel.
He left Sauber in 2009 and had spells in F3 and the DTM before joining the Porsche WEC team as head of track engineering in 2012, working alongside Seidl.
He returned to BMW in an engineering role in 2014, rising to the position of head of race and test engineering, operations and organisation in 2018.
Krack will work under the direction of team owner Lawrence Stroll and Group CEO Martin Whitmarsh, who was appointed late last year.
Marcin Budkowski, whose departure from Alpine was announced yesterday, had earlier been linked with an Aston role.
"Aston Martin is one of the greatest automotive brands in the world," said Krack.
"And to have been asked to play a leading role in delivering the on track success that such an illustrious name so richly deserves is a challenge that I plan to embrace with energy and enthusiasm.
"I have been working in motorsport for over 20 years, and worked in F1 with Seb Vettel in 2006 and 2007 when I was a BMW Sauber engineer and he was the team's test driver.
"I have huge respect for his speed and ability, and it will be fantastic to be reunited with him. Lance Stroll is a seriously fast and talented driver, too, with 100 Grands Prix starts to his name, and I am very much looking forward to working closely with him.
"Team Silverstone has always impressed me. It is full of talented people and real racers. That racer's culture and values are what is required to succeed in motorsport - I know that and my new colleagues at Aston Martin know it, too. We will work incredibly hard. We want to win. Together, we will."
Whitmarsh said: "Mike Krack is exactly the right kind of dynamic and modern Team Principal who, working with our other senior leaders under Lawrence's and my overall direction, as well as with our ever-growing staff of skilled and committed employees, will deliver the F1 world championship success that we at Aston Martin are so determined to achieve.
"Having worked in very senior motorsport positions at both BMW and Porsche, backed by an engineering background in F1 with Sauber, Mike possesses a blend of experience and expertise that makes him the ideal choice for us.
"He works well with drivers, having prioritised that aspect of his role at BMW in recent years, and also with engineers, since he speaks their language."
Lawrence Stroll added: "We are hiring brilliant new people every week. Our new factory build is coming along very well. We have a fantastic roster of superb sponsor partners. We are about to embark on year two of our five-year plan, the objective of which is to win F1 world championships.
"All the ingredients we require are coming together. Mike will play a central and leading role, reporting to Martin Whitmarsh and leading our technical and operational functions, our collective aim being to fulfil those lofty ambitions. We are on our way."
BMW has acted swiftly to appoint Krack's successor by naming Andreas Roos as its new head of motorsport programmes, starting from 1 February.
Roos has been recruited from Audi, who was previously in charge of its DTM efforts before taking on the project management of its factory motorsport division, including its upcoming LMDh project and Dakar Rally programme.