Chris Coleman's team, featuring in a major tournament for the first time since the 1958 World Cup, exceeded all expectations by reaching the semi-finals in France before being knocked out by Portugal.
Fans greeted the players and backroom staff at Cardiff Airport before the squad went on an open-top bus parade through the city.
"They are amazing scenes and we'll never forget," said talismanic forward Gareth Bale. "It's very special seeing what it means to the whole country.
"It's an incredible feeling and there is no prouder honour than putting on the red shirt for Wales and to share it with all these fans is incredible."
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Midfielder Aaron Ramsey was also moved by the welcome home.
"To see all the support has been phenomenal," said Ramsey. "Because we have been away from it we haven't seen the impact it has had back here.
"We have heard from our families and stuff like that...but this is the first time we are experiencing any of this and it is really special."
One member of the squad who missed out on the homecoming was midfielder Joe Ledley, who is in Ibiza to get married.
"We are so proud of what we have done," said captain Ashley Williams. "We would never have thought it would create this big an impression.
"It is quite emotional really, a feeling of pride at what the lads and the staff have achieved."
(Writing by Tony Jimenez; Editing by Andrew Both)
