Now that it has happened, it seems an obvious trick for England's director of cricket to have performed. Bayliss has an enviable track record both internationally and domestically, in five-day, four-day, one-day and Twenty20 cricket. He is an unassuming chap with a deep knowledge, a quick mind and a vision about how the modern game should be played.
He will begin - the unveiling has yet to be formalised since Bayliss is still in Sydney - without much recent knowledge of England's players or conditions here. But that should be offset by his relationship with the assistant coach, Paul Farbrace, who is standing in following the sacking of Peter Moores.
When Bayliss was appointed coach of Sri Lanka in 2007, he invited Farbrace, whom he had come to know on coaching courses in Australia, to be his assistant. The pair hit it off and had a fruitful partnership. Both men were on the Sri Lanka team bus that was attacked by terrorists on its way to the Gaddafi Stadium in Lahore for a Test match in 2009 but escaped injury.
Farbrace will provide a perfect sounding board for Bayliss when he arrives. It will ease the introductions, for Farbrace is hugely popular in the England dressing room.
Bayliss is understood to be England's first choice, ahead of the clear favourite Gillespie, who knows many of the England team well. The former Australia fast bowler has impressive credentials, but he also had understandable reservations concerning his young family and the sheer relentlessness of the England job.
Bayliss, who comes from the small town of Goulburn, played 51 matches for New South Wales as a batsman between 1986 and 1992. He had one truly productive season, in 1989-90, when he scored 901 Sheffield Shield runs at an average of 56.31.
But it was as an astute coach, with a good eye, that he was to make his name. He started out as a development officer in New South Wales, became the state's assistant coach and then, in 2004, was made coach. In his first season, New South Wales won the Sheffield Shield and in his second the state one-day trophy.
Bayliss secured the Sri Lanka job against the odds. He took his time to settle and to gain the trust of the dressing room, but he did both and helped Sri Lanka to make the best of themselves, winning five of their 11 Test series under him, including victories against India, Pakistan and England, and reaching their highest place in the ICC rankings. He helped them to the finals of the World Twenty20 in 2009 and the World Cup in 2011.
He returned home after four years, eager for a change of pace. But by now, with such a welter of experience, he was a coach at the top of his game. He won the inaugural Big Bash with Sydney Sixers in 2011 and then the Indian Premier League with the under-achieving Kolkata Knight Riders in his first season in 2012 and again two years later.
Part of Bayliss's appeal to Strauss is, undoubtedly, that he has a good track record in limited-overs cricket. The fact that Moores was deemed to be off the pace in the rapidly evolving contemporary game was part of the reason for his sacking.
This will be a big move for Bayliss but Strauss was right last week when he implied that the England job was too big to turn down.
It may turn out to be a case of better late than never. Bayliss was approached when England were searching for a replacement for Andy Flower last year, only for Moores to be appointed for a second time.
Bayliss said later, on the Cricinfo website: “I was up front with them. I wasn't chasing it, they were the ones ringing me. I was quite happy doing what I'm doing.”
Now they have chased him again.
ECB'S CHOSEN ONE TREVOR BAYLISS'S CV
58 first-class and 50 List A matches for New South Wales. Scored 3,060 runs at average of 35.58.
Start of coaching career
After retiring, he became a cricket development officer for NSW Cricket Association and was long-term second XI mentor before taking top job in 2004.
New South Wales
Won Sheffield Shield titles in 2005 and 2014.
Reached 2011 World Cup final.
Won Big Bash League and Champions League in 2012.
Kolkata Knight Riders
Won IPL in 2012 and 2014.
Won T20 series against South Africa in 2014. – The Independent
Original source: Bayliss set to be named England coach