The forward, who along with Southampton team mates 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 joining Southampton 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 over Moldova, 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.
“I’ve been suffering with my sleep and getting up in the middle of the night because I’m just lying there thinking about the possibility of going to the World Cup.
“Over the last week, I’ve been sleeping less and less and last night it was virtually impossible because my head was everywhere.
“I wasn’t in a good place because I was dreading the phone call, so when I finally got told today it was a dream come true.”
Turning his focus on his club team mates Lallana and Shaw, Lambert added: “I was more than confident that Adz (Lallana) was going to get in because he fully, fully deserved to.
“I think he’s fighting for a starting place with how well he’s done.
“At first I wasn’t too sure about Luke Shaw because (Chelsea’s) Ashley Cole was obviously the best left-back over the last 10 years, as Luke has said himself.
“When we heard the news last night that (Cole) had been dropped, our first thought was that Luke had to be in.
“What he has done is frightening, and his mental strength is second to none for a young lad. He’s not going to be overwhelmed by anything that comes his way.”
(Writing by Ossian Shine; Editing by Ken Ferris)