Nilsson had formed section of a two-pronged senior team management structure, the renowned engineer splitting the role with commercial chief Bruce Stewart.
However, included in what the team has described as a streamlining process due to the aftereffects of the coronavirus pandemic, Nilsson will leave his post effective straight away.
Stewart will take over as the sole team principal, while former British Touring Car Championship-winning engineer Carl Faux will assume the lead tech role.
“Like every responsible sporting organisation, ensuring the viability of our team, now and into the future, has been the key focus of ours over the last couple of months, which is why we now have reached your choice we have,” said team part-owner Ryan Walkinshaw.
“Tough decisions must be produced in the current climate.
“2020 has changed the global sporting landscape, with every reputable organisation forecasting and restructuring for the backend of the year and beyond, and we are no different.
“We’ve agreed now so that Mathew has the most useful opportunity to look for a new role, whether that be in Supercars or beyond.
“I personally wish to thank Mathew for his contribution to the team for a very any period of time of time, I have really enjoyed working with him, and feel he will be an asset to any business in the future.”
The rest of the WAU ownership group agreed it had been a tough, but ultimately unavoidable, outcome.
“2020 has meant that we, like many other teams, have had to consider our structures and make the necessary decisions required to ensure the sustainability long-term, which can be paramount,” said Michael Andretti.
“While difficult decisions need to be made, it’s the responsible thing to do not just for our team and fans, but the sport itself.
“Thank you to Mathew, and we wish him all the best with his future endeavours.”
Zak Brown added: “With current circumstances, your decision was essential to ensure the and viability of the team for the remainder of 2020 and well to the future.
“Having a commercially minded team leader in Bruce, is important, now inside your.
“We all wish Mathew all the best with his future, and appreciate his efforts with the team.”