Giggs' appointment comes following Chris Coleman's resignation in November, while the 44-year-old was previously linked with managerial vacancies at the likes of Swansea City.
The former Red Devils' winger made 64 appearances for the country between 1991 and 2007, but never managed to reach a major worldwide tournament.
Giggs said he will speak to Coleman's assistant Osian Roberts - who was an unsuccessful candidate for the job alongside Craig Bellamy and Mark Bowen - over whether the FAW's technical director will be part of his coaching staff.
Scholes helped Giggs out when he took interim charge of United after David Moyes was sacked in April 2014.
Newly appointed football manager of Wales, Ryan Giggs poses for photographers at the Hensol Castle hotel, south Wales on 15 January 2018.
Former Wales captain Giggs told last month that he could be tempted back into football management with the national team.
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Giggs said he had picked the brains of his former boss at Old Trafford, under whom he spent nearly his entire career.
"When I took over at United for those four games [in 2014], I felt comfortable", he said.
I should be the proudest dad in the world, as happy as a lark by what he's achieved - but I am ashamed of him.
I can't even bring myself to use his name - I refer to him as the ex-footballer. "But I think that's down to the individual".
Giggs then attempts to issue a rallying cry to get the team to end the season on a high. "He's one of the greatest managers of all time".
"I can't wait to start working with the players as we prepare for those crucial games later in the year".
"There'll be stressful times, ups and downs like when you're a player but I want to enjoy it - hopefully we will have some fun along the way, too".