The 44 year old had long been a target for the Football Association of Wales (FAW).
The FAW confirmed the appointment on social media and in a statement Giggs said: "I am so proud to have been given the honour of managing the national team.
"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."
FAW chief executive Jonathan Ford said: "With his vast amount of experience having played, coached and managed the biggest club in the world, we are confident of a successful future for our national team."