Marshall, who held the chief engineering officer title at Red Bull, will join McLaren in January as technical director, engineering and design.
Only two months ago, when McLaren announced a restructuring based on three technical directors, that job was given to Neil Houldey.
After it became apparent that Marshall could join the team, Houldey agreed to step aside and become his deputy.
"Neil has always been part of the process," said Stella when asked by Autosport about the change of plan. "He's been in the conversation, he has actually played as a team player in this process.
"And when we told Neil that we had this opportunity, which was quite unmissable, we elaborated together the solution.
"There's so much to do in terms of engineering and design to create the right standards to design the fastest car in F1 that actually, we thought this is a very powerful combination with Rob, the more of the technical authority, and Neil running more of the day-to-day activities within the department.
"So definitely Neil was in the process, a very constructive process."
Expanding on what Marshall will bring to McLaren, Stella said: "Rob will join the team with a unique level of experience and know-how in terms of engineering and design of F1 cars.
"He has also been instrumental in creating such a strong technical department at Red Bull.
"So at the moment, we are just very pleased and excited that Rob is keen to join our journey to take McLaren to the front of the grid."
When McLaren announced Marshall's signing, Red Bull issued its own statement, which acknowledged his contribution and wished him well, indicating that his departure is not accompanied by the sort of animosity that sometimes occurs when a key player leaves a top team.
Stella suggested that tone was a reflection of the respect in which Marshall is held in the Milton Keynes camp after some 17 years with the team.
"Certainly Rob was very keen to join McLaren," said Stella. "He understood perfectly our journey, our ambition.
"I think he understood that he could be a fundamental player in trying to make something important like bringing McLaren to victory. So strong motivation from his side.
"I think at Red Bull they know very well the role that Rob played over time. And I think this invokes respect for people. And if I put what I could judge from outside I saw this level of respect from Red Bull to Rob, which observing, was good to see.
"And then when it came to the press release that was obviously agreed between the teams. That's why it was coordinated."
