Alexander-Arnold had to endure a nervous wait before learning he had made the cut after spending much of the season out of favour with Southgate.
The 22-year-old was left out of Southgate's England squad for their World Cup qualifiers in March.
But Alexander-Arnold's strong end to the season with Liverpool convinced the England manager to restore the right-back to his squad for Euro 2020, which starts on June 11.
Manchester United forward Lingard, who had a superb loan spell with West Ham, was the highest profile casualty as Southgate axed six players from his provisional squad.
The 28-year-old was recalled to the England squad in March after a long exile.
His brilliant form, including nine goals in 16 games, earned the Hammers a place in the Europa League, but it wasn't enough to convince Southgate of his worth.
"For me personally, it was very difficult to speak to Jesse, who has given so much to England," Southgate said.
The others to miss out were Sheffield United keeper Aaron Ramsdale, Southampton midfielder James Ward-Prowse, Aston Villa striker Ollie Watkins and uncapped centre-backs Ben Godfrey and Ben White.
'A lot of talent'
One selection decision was taken for Southgate on Tuesday morning when Manchester United forward Mason Greenwood pulled out with what his club said was an "underlying injury".
Southgate said the six players he has left out will be available to play in England's friendlies at Middlesbrough against Austria on Wednesday and Romania on Saturday.
"I think every squad is difficult because we have a lot of talented players in this country," Southgate said.
"The most difficult thing is to not be able to take players who've been with us in previous matches and who are such good professionals.
"We're not taking any tourists. We've got a squad ready to play."
Alexander-Arnold faces intense competition, with Kyle Walker, Kieran Trippier and Reece James among four right-backs included in the squad.
Trippier helped Atletico Madrid win the Spanish title this term, while Walker was instrumental in Manchester City's Premier League triumph.
Walker was on the losing side as Chelsea's James gave a dynamic display in the Blues' 1-0 win against City in the Champions League final on Saturday.
Southgate had originally been due to officially announce his squad last week.
But instead he named a 33-man provisional group, delaying his final decision until the June 1 deadline.
That gave Harry Maguire, Jordan Henderson and Kalvin Phillips time to prove their fitness.
Manchester United defender Maguire had been struggling with ankle ligament damage suffered at Aston Villa in May.
The injury forced him to miss the Europa League final defeat against Villarreal last week.
Liverpool midfielder Henderson has not played since having surgery on a groin injury in February.
"The most complex part this time has been those injuries and whether we should take the chance on people," Southgate said.
"We've clearly with Jordan and with Harry Maguire, we've got a couple of players who are not where we'd be ideally in terms of their physical prep.
"But we think that the experience they have, the fact that we think we can get them to a point where they can have an involvement in the tournament, it's worth taking them, especially as we've got an extended squad of 26."
The Three Lions begin their Euro 2020 campaign against Croatia on June 13 before facing Scotland and the Czech Republic in Group D.
England's 26-man squad for Euro 2020:
Goalkeepers: Jordan Pickford (Everton), Dean Henderson (Manchester United), Sam Johnstone (West Brom)
Defenders: Luke Shaw (Manchester United), Harry Maguire (Manchester United), Ben Chilwell (Chelsea), Reece James (Chelsea), John Stones (Manchester City), Kyle Walker (Manchester City), Tyrone Mings (Aston Villa), Conor Coady (Wolves) Kieran Trippier (Atletico Madrid/ESP), Trent Alexander-Arnold (Liverpool)
Midfielders: Declan Rice (West Ham), Jordan Henderson (Liverpool), Kalvin Phillips (Leeds), Mason Mount (Chelsea), Jude Bellingham (Borussia Dortmund/GER)
Forwards: Phil Foden (Manchester City), Raheem Sterling (Manchester City), Jack Grealish (Aston Villa), Harry Kane (Tottenham), Marcus Rashford (Manchester United), Jadon Sancho (Borussia Dortmund/GER), Dominic Calvert-Lewin (Everton), Bukayo Saka (Arsenal)