Clarke confirmed the call-up on Sunday as Scotland's squad departed Glasgow Airport for their pre-tournament training base in Florida, hours after Napoli midfielder Billy Gilmour was confirmed as ruled out of the tournament with the knee injury he sustained in Saturday's 4-1 friendly win over Curaçao at Hampden Park.
"For myself, it was a really difficult night," Clarke told reporters. "I haven't slept much, I have to be honest. I had to disappoint another three players this morning again, to tell them that they had missed out."
The three bypassed were Connor Barron of Rangers, Sparta Prague's Andy Irving and Udinese midfielder Lennon Miller — all of whom had been capped before and named on standby when Clarke announced his original 26-man squad.
Manchester United midfielder Fletcher, 19, had not been in that official standby group. He was among five young players added to the training camp for experience during the pre-tournament sessions. He then found himself making his senior debut as a half-time substitute after Gilmour went off with his injury — and produced an impression Clarke could not ignore.
"I just felt Tyler came into the squad this week and showed up really well, did well in the game, so that was the thinking behind that one."
Fletcher has accumulated just 17 senior minutes for United in the Premier League. His twin brother Jack has opted to represent England at youth level.
John McGinn, whose Aston Villa side won the Europa League last month, said the camp had been left with a bittersweet mood as they headed to America.
"Obviously our first thoughts this morning are with Billy. He is a huge part of the group, a big part of the country moving forward. We are devastated for him."
McGinn also spoke warmly about the Fletcher family legacy — he played with Tyler's father Darren Fletcher early in his Scotland career.
"I played with his dad, Darren, so it is an amazing day for his family. He is not just here to make up the numbers. He is here to impress and hopefully help us, not only now but in the next 10 to 15 years."
Scotland open their World Cup campaign against Haiti on June 14 and also face Morocco and Brazil in Group C. It is their first World Cup since France 1998.