The forward, who along with Southampton teammates Adam Lallana and Luke Shaw was named in Roy Hodgson's 23-man squad for the finals, said it was an occasion to be treasured.
"There have been a lot of proud moments over the last five years, but I think today has topped it all off," the 32-year-old told the south coast club's website.
"To finally get the call is more than I could have ever dreamed of because I could never have expected this two years ago, let alone 10 years ago. This is more than a dream.
"There's elation, pride, joy - everything."
Lambert, who bounced around several clubs in the lower reaches of English soccer before joiningSouthampton in 2009 when they were in the third tier, made his England debut last year, scoring against Scotland in a 3-2 friendly win.
He caught the eye again in his second international, scoring in a World Cup qualifying victory overMoldova, and calls for his inclusion in Roy Hodgson's squad began to grow.
"Through the last few months, the best thing to do was to try not to think about it, but it comes to a stage where the nerves overtake you and it's hard to get a grip of them," he said.