White, who was in the Euro 2020 squad but did not play, had missed out on recent call ups, including for last month's Nations League fixtures.
The versatile 25-year-old has been in fine form this season as Premier League leaders Arsenal mount a title challenge, and was rewarded on Thursday after being named alongside team mates Bukayo Saka and Aaron Ramsdale in Southgate's 26-man squad.
"He was very happy and the rest of the squad were so happy for him. He fully deserves it and you could see it was a big moment for him," Arteta told reporters on Friday.
"All the credit is down to him and what he's done. If you look at his career and how far he's come in a very short period of time it shows everything about the person, the player, his ambition and everything he's done in the last two years."
Arsenal have 34 points from 13 games ahead of the visit to Wolverhampton Wanderers, who are 19th with 10 points, on Saturday in their final game before the pause for the World Cup.
Arteta's side, two points ahead of champions Manchester City, will definitely head into the break top if they beat Wolves but the Spaniard would not be drawn on the title race.
"I'm not here to give opinions on that. What I want to do is finish as high as possible."
Arteta's former City boss Pep Guardiola labelled the London side as rivals for the league crown, however, and lauded the Arsenal boss for their superb start to the season.
Guardiola, who Arteta worked with as an assistant coach from 2016-19 before taking over at the Emirates, insisted Arteta deserved all the credit himself.
"I'd like to say (there's) a lot (of influence), but I'd lie to you," Guardiola told reporters on Friday. "Maybe I learned more off him than he did off me when we worked together.
"Arsenal have the work ethic, the talent, the support. People see how he works every day, the commitment... We have has an incredible season, they have been better. For sure they are contenders."
