The French giants, whom Byrne joined in 2011, were tested all the way by Munster on Saturday but held on to reach their first final.
And Byrne, who has already racked up a British & Irish Lions tour and 46 Welsh caps, including a RBS 6 Nations Grand Slam, was thrilled with the accomplishment.
He is now aiming to become just the ninth Welshman to lift the biggest prize in European club rugby.
“It is a dream come true for me to finally reach a European Cup Final,” said Byrne.
“But you can’t take anything away from Munster – they wore their famous red jersey with real pride.
“It was the toughest game we have had all season and you’ve got to hold your hands up to Munster for that. We had a few opportunities, but the ball didn’t stick.
“We got a bit nervy, but hopefully we will come back stronger for the Final. Whoever we face we will do out homework and come out firing.”
Byrne and Clermont Auvergne will face French rivals Toulon in Dublin on Saturday, 18 May.
Welsh Heineken Cup winners.
Tony Rees (Brive, 1996), Ieuan Evans, Nathan Thomas, Richard Webster (Bath, 1997), Andy Newman, Allan Bateman (Northampton Saints, 2000), Rob Howley (London Wasps, 2004) and Gareth Thomas (Toulouse, 2005).
