Beaumont is now a leading administrator in world rugby and becomes a CBE, having been awarded an OBE on his retirement as a player in 1982.
"It is fantastic that Lawrence and Bill Beaumont have both been honoured and it is excellent news for the sport of rugby union in England," said Andrew, ahead of England's Test against New Zealand in Auckland.
"Lawrence thoroughly deserves his award and it recognises the huge contribution he has had made to his club, country and the British and Irish Lions over the last dozen years.
"Lawrence was the only player to play in every minute of England's campaign in the 2003 World Cup and he played a key role in that success. He has had an outstanding career.
"Bill is a superb ambassador for our sport not only in England but worldwide, where he holds the support and respect of his peers at all levels of the game."
Beaumont, 56, follows Martin Johnson as only the second recipient of a CBE for services to rugby union in England.
He won 34 caps for England and, in 1980, captained his country to their first Five Nations Grand Slam in 30 years.
Beaumont found popular fame as a captain on BBC television's A Question of Sport but he has remained heavily involved in rugby union.
Beaumont was manager of the 2005 Lions tour to New Zealand, he represents the RFU on the IRB council and is director of the Six Nations and the Rugby World Cup.
The CBE was also awarded in recognition of Beaumont's charity work. He is honourary president of rugby charity Wooden Spoon and is also involved with SPARKS, the Lord Taverners and the United Nations Food Programme.
"I am honoured and delighted. I was fortunate enough to receive an OBE for playing the game in 1982, and now 26 years later to get this award for other things which I have managed to achieve makes you feel very humble," he said.
Dallaglio receives the OBE having been awarded an MBE after England's 2003 World Cup triumph.
Dallaglio spent his entire rugby career at Wasps and helped establish the club as one of Europe's leading forces in the professional era.
In nearly two decades at Wasps, he won five league titles and two Heineken Cups. Dallaglio won 85 England caps and was selected for three Lions tours.
Beaumont added: "Lawrence has been an outstanding player for England and an outstanding leader.
"To end up winning the Premiership final as the culmination of his career was very fitting."