The group achieved worldwide record sales of more than 200million during their career and had five No1 hits in the UK.
Gibb, 71, said: "I am deeply honoured, humbled, and very proud. This is a moment in life to be treasured and never forgotten.
"I want to acknowledge how responsible my brothers are for this honour. It is as much theirs as it is mine. The magic, the glow, and the rush will last me the rest of my life."
Former Beatles drummer Ringo Starr had been tipped for a knighthood several times, including by his former bandmate Sir Paul McCartney, who said in 2011 that it was "about time".
The 77-year-old acknowledged his knighthood with a short message, signed off with his trademark phrase "Peace and love". He said: "It's great! It's an honour and a pleasure to be considered and acknowledged for my music and my charity work, both of which I love."
Ringo was once jokingly described as 'not even the best drummer in the Beatles'. The quip is often attributed to John Lennon but never verified. In 2011, Rolling Stone readers named him the fifth-greatest drummer of all time.
Starr maintained a high public profile through his narration over 1984–86 of the popular TV children's series Thomas & Friends, based on the Thomas the Tank Engine series of books.
Actor Hugh Laurie, 58, renowned for his Fry and Laurie shows, Blackadder, House and The Night Manager, former British Vogue editor Alexandra Shulman and chef and television presenter Rick Stein all received CBEs.
Actresses Susan Hampshire, 80, who starred in Monarch of the Glen and The Forsyte Saga, and Julia McKenzie, best-known for the sitcom Fresh Fields and as Miss Marple in several Agatha Christie dramas, also received CBEs.
Breakfast television host Eamonn Holmes, 58, was awarded an OBE for services to broadcasting, and said it was 'a wonderful accolade".
He said: 'It's like getting a gold star for your homework – 2018 will be my 38th year as a broadcaster and I can't think of a better way of marking that.'
He added: "It's lovely to have someone in authority say, "You know what, you do this quite well"."
Singer Marc Almond – best-known for the 1980s hit Tainted Love with Soft Cell – said he felt 'incredulous shock' after learning he was being awarded an OBE, adding: 'I can't really be a rebel any more.'
Veteran Scots actor James Cosmo, who appeared in films including Braveheart, Trainspotting and Highlander and in hit show Game of Thrones, was awarded an MBE.
Away from the limelight, Craig Mackey, the deputy commissioner of the Metropolitan Police Service, received a knighthood and there were honours for several entrepreneurs.
Businesswoman Vivian Hunt was given a damehood and married couple Chrissie Rucker, founder of The White Company, and Nicholas Wheeler, founder of Charles Tyrwhitt Shirts, both received OBEs for services to retail.
The two oldest recipients were both 101 – Lt Col Mordaunt Cohen, who was awarded an MBE for services to education about the Second World War, and Helena Jones who was given a British Empire Medal (BEM) for her work with young people.
The youngest, Lucia Quinney Mee, was just 18 and was also awarded a BEM for her campaign work on organ donation after she underwent three liver transplants.
Seventy per cent of this year's 1,123 honours were awarded for 'outstanding work in the community' following criticism that recent awards have been dominated by political rows.
There were no awards for those who volunteered to help in the aftermath of this year's terror attacks or the Grenfell Tower fire but Cabinet Office sources said they would be honoured in the future.
