Aaron Ramsey was the hero in Cardiff, scoring a goal in each half as Wales clinched the second qualifying spot behind Croatia in Group E – earning a shot at matching their Euro 2016 exploits following a semi-final run.
An uneven start to his first campaign in charge meant Giggs' men needed to win both of their closing matches to progress.
Victory in Azerbaijan over the weekend before success in front of their fervent home support saw them come good when it mattered.
"It's doesn't get any better," Wales manager Giggs told Sky Sports. "It's amazing. From where we were in the summer with those two defeats [away to Croatia and Hungary], credit to the lads the way they've come back.
"They've show grit, determination and quality. It's one of the best days of my life."
Ramsey's injury problems meant the Juventus star was making his first start of qualification on Tuesday but he very quickly made up for lost time.
"He's just showed that quality, that class," Giggs said. "The finishes...we missed him, but better late than never, I suppose."
Having never managed to represent Wales at a major tournament as a player, Manchester United great Giggs will revel in leading his country on such a grand stage.
"To be honest I haven't really thought about that," he added, referencing those playing disappointments.
"It's one of the greatest days of my life. There was a lot of hard work put in. Not only am I blessed with a good set of players but also the best staff I could ask for.
"The atmosphere every time we play in Cardiff...the fans are part of it. I was watching it in 2016 – you could tell the fans loved it then and they'll love this even more."
Wales finished qualification as second in Group E, one point clear of Slovakia and three points shy of group winners Croatia.
Giggs' side won four of their eight qualifiers with two draws and two losses making for an ultimately successful campaign.