The Manchester City striker has hung up her boots at the age of 33, with 52 goals in 113 caps and a Euro 22 winners' medal, plus a slew of domestic honours to her name.
White played a vital role in England's Euros triumph, starting all six games and scoring two goals in the record-breaking 8–0 victory over Norway.
"Ellen has given so much for England and we are all so proud of her," said Wiegman.
"I have only had the pleasure of working with her for this past year, but her professionalism, work rate and finishing ability is world-class.
"This summer she did an amazing job for the team, she is the perfect team player and helped the younger players to find their way in international football.
"I already knew she was a great player but I found an even better person.
"We will miss her, but I fully understand her decision to take a new direction."
White admitted her football "dreams came true" in winning Euro 2022 but insisted it was the right time to call it quits.
She had agonised over retiring, but eventually felt England's glittering summer would prove the ideal time to bow out.
"This has been one of the hardest decisions of my life but one that I know is the right decision for me," said White.
"This decision has always been one I have wanted to make on my terms. And this is my time to say goodbye to football and watch the next generation shine.
"It has been my greatest honour and privilege to play this game. In particular playing for England has and always will be the greatest gift.
"My dreams came true on July 31, winning the Euros and becoming a European Champion."
White came through Arsenal's academy but made her name at Chelsea, spending three years in the Blues' senior ranks before heading to Leeds.
After returning to Arsenal, stints at Notts County, Birmingham and Manchester City all followed.
The Lionesses have been determined to capitalise on their success to force change at every sporting level, to boost sporting opportunities for girls and women.
And White urged future England hopefuls never to lose sight of their dreams.
"This is for the next generation and potentially the next Lioness," said White.
"You don't have to be the best at something to make your dreams come true, just look at me.
"Hard work, dedication, passion and love for what you do are a great recipe. Don't ever let someone tell you 'you can't do something or achieve your dreams'.
"I was once told I couldn't play in the boys' team and I would never play for England. Now I am retiring having made 113 caps with 52 goals for England and a European Champion.
"Finally, let's use the momentum from the Euros win to make sure that every young person in all communities has the opportunity to play and feel connected to all England football teams."
Baroness Sue Campbell hailed White as the epitome of a role model for future generations to emulate.
"Ellen White will long be remembered as a model for others to follow," said Campbell, the FA's women's football director.
"It is not just about her record-breaking 52 goals and performances on the pitch, but about the standards she set and the way she conducts herself.
"A true leader of women, it has never been about Ellen White for her - even when she was scoring the crucial goals or giving everything she had, it was always the team first. She is a legend of the modern game."