The 58-year-old former Test batsman was one of the most respected figures in the world game and it had been suggested he could take over as England coach once his contract expired with Pakistan in June.
Woolmer's Pakistan team crashed out of the World Cup less than 24 hours before his death by losing to debutants Ireland at Sabina Park, Kingston, Jamaica.
The tributes were led by the head of the sport's governing body, International Cricket Council chief executive Malcolm Speed.
''On behalf of the ICC and Bob's thousands and thousands of friends within cricket, I wish to express my very sincere condolences to Mrs Woolmer and the family on Bob's very untimely passing,'' he told a news conference in St Lucia during England's match with Canada.
Woolmer worked for the ICC as a coach to the minor nations, including Ireland, between 2001 and 2004.
Speed said: ''In some ways we could say yesterday's loss when Pakistan lost to Ireland was a great defeat for Bob and the Pakistan team. But for Bob, there is another way of looking at it, it was a great triumph.
''He was a great cricket man.''
One of the first to pay tribute was South African team manager Goolam Rajah.
''I was very close to him. I had the greatest respect for him as a man and a coach. We have all got to go but not like this.
''I just spoke to him a few days ago in Trinidad. We held him in the highest regard. He was a wonderful coach and he made a huge difference to South African cricket.
''Our thoughts and prayers are with his family.'' Woolmer had been South African coach from 1994 until the 1999 World Cup in England.
South African fast bowler Shaun Pollock, a former skipper, said he was stunned by the news.
''My prayers and thoughts are with his family. Bob was a friend and a fantastic coach who had a huge impact on my career.
''He was passionate about the game and always looking for ideas and possible innovations to improve individuals and teams.
''He still had so much to offer the world of cricket and will be sorely missed. I was very fortunate to have played under him for South Africa and Warwickshire.'' A former England Test team mate Dennis Amiss added: ''The game has lost a lovely man and a top coach.''