"Never in my 25 years as a manager have I been so well supported in my role," he said.
Attention now turns to whether Giggs will also leave the club - with the intention of cutting his managerial teeth elsewhere - or opts instead to serve as an assistant to a third United manager in Mourinho after two testing experiences under David Moyes and van Gaal.
With Mourinho expected to bring trusted lieutenants Rui Faria and Silvino Louro with him in addition to another assistant, Giggs runs the risk of having little more than a ceremonial role under the Portuguese.
The prospect of Giggs leaving the club he joined on his 14th birthday, going on to become its record appearance maker and the most decorated footballer in British history, would signal another significant severing of ties from the Sir Alex Ferguson era.
The squad Ferguson left behind when he retired three years ago has had a dramatic overhaul and more upheaval is expected as Mourinho plots a 200 million spending spree.
Giggs had previously indicated in private that he would walk away if he was not offered the manager's job and sources close to the 42-year-old said he faced a serious dilemma.
Giggs visited George's restaurant and bar in Worsley, which he owns, as he pondered his next move. He is thought to be bitterly disappointed but also recognises that if he chooses to leave the club and struggles as a manager elsewhere that it could damage or kill his prospects of one day taking charge at Old Trafford.
Giggs saw Gary Neville, his close friend and former United teammate, try his hand at management at Valencia recently and fail, and has also seen the struggles of Patrick Vieira at New York City FC, sister club of Manchester City. Giggs has been encouraged to try his hand at another club first by Peter Schmeichel.
"I think it's very important that Mourinho has an assistant who knows the club," the former United goalkeeper said. "[But] it would be so good for [Giggs] to have had a job somewhere else ... and if he is successful he can come back and manage United."