The FAW confirmed Giggs' appointment via its official Twitter feed with a short film of a Wales shirt having the name 'Giggs' pressed into it, with an accompanying caption of #CroesoGiggsy (Welcome Giggsy).
It will be Giggs's first permanent managerial post and he succeeds fellow former Wales international Chris Coleman, who bowed out after the national side failed to qualify for this year's World Cup finals in Russia and now manages English Championship side Sunderland.
"I am so proud to have been given the honour of managing the National Team," said Giggs in a FAW statement.
"The challenges that we have ahead of us with the Nations League and qualification for UEFA EURO 2020 excite me a great deal.
"I can't wait to start working with the players as we prepare for those crucial games later in the year."
Giggs' first fixture in charge of Wales will be in the 2018 China Cup against the hosts in Nanning on March 22.
Mourinho claims £300m not enough to win league
This will be Giggs's first full-time job as a manager, although he was in caretaker charge of United for four games at the end of the 2013/14 season after David Moyes was sacked.
Giggs, 44, has been the clear favourite for the Wales job since he declared his interest last month, saying: "I've played for Wales and I've said that I want to go back into coaching.
"Obviously that is one of the top jobs."
Giggs was interviewed last week along with former international team-mate Craig Bellamy and Osian Roberts, Coleman's former assistant who is also the FAW's technical director.
Former Wales defender Mark Bowen was also interviewed after leaving his role as Stoke's assistant manager a few days earlier.
Giggs's contract, which will reportedly take him up to the 2022 World Cup, was tied up over the weekend.
Swansea pin hopes on new manager bounce
The FAW was keen to make the appointment before the UEFA Nations League draw, which takes place in Switzerland on January 24.
Giggs, who won 64 Wales caps between 1991 and 2007, has been out of football for 18 months since leaving the coaching staff at Manchester United.
He spent two seasons as Louis van Gaal's assistant coach, but he left Old Trafford in the summer of 2016 following Jose Mourinho's appointment as manager.
That ended a long association with the club where he made a record 963 appearances as a player, scoring 168 goals.
Coleman spent nearly six years as Wales manager before leaving to take over relegation-threatened Sunderland in November.
He became the most successful manager in Welsh football history when he guided the country to the semi-finals of Euro 2016 -- Wales's first major tournament for 58 years -- only to suffer the heartache of missing out on the World Cup.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ