Vowles left Mercedes, where he was highly regarded as its strategy director, to head up Williams after the departure of former team principal Jost Capito.
The move was endorsed by Mercedes chief Toto Wolff, who said he had "no doubts whatsoever" that Vowles "has all the necessary skills to become a fantastic team principal".
Williams driver Alex Albon said he was excited about Vowles' arrival as everyone at Mercedes "speaks very highly of James", including his friend Russell, with whom he had discussed the change.
"Firstly, really happy for James. I think he thoroughly deserves the opportunity," said Russell, speaking at the launch of Mercedes' W14 2023 car.
"I can't think of anybody better Williams could have hired for the job they need to undertake."
Russell raced at Williams for three years at the start of his F1 career and acknowledged that Vowles will have his work cut out to guide the Grove team back towards a competitive place in the midfield.
"I'm sure he's going to have a few surprises when he goes to Williams, naturally when you've spent so long at such a team with so many championships under his belt," he added.
The 25-year-old thinks Mercedes is in a good place despite Vowles' departure, as the Brackley team has been proactive in its succession planning.
"I think for us on a strategic level, when it came to race strategies, James had already sort of handed over his duties to others within the team and he was just overseeing," Russell explained.
"But actually, throughout all of last year, the decisions were being made by others. So in that regard, I think James has left us in very competent hands."
Mercedes is expected to hand over Vowles' duties to several staff members rather than appointing a direct replacement.
Meanwhile, Vowles has committed to strengthening Williams' technical team while empowering its current employees and improving the company culture.