White's inclusion was announced by the Football Association on Monday morning as the team continue preparations for their European Championship opener against Croatia.
White made his debut in last week's 1-0 friendly win over Austria and impressed as he started alongside Tyrone Mings in Sunday's victory against Romania.
He tweeted: "Beyond proud and honoured! I'll give it my everything @England."
Alexander-Arnold was ruled out after suffering a thigh injury late on against Austria and Southgate took his time to decide which of his standby players would come in.
Everton defender Ben Godfrey and Southampton captain James Ward-Prowse were other options who both started the Romania game, while Jesse Lingard and Ollie Watkins were also on the standby list, but will now return home.
Euro 2020 kicks off on Friday night, with England's clash with Croatia taking place at Wembley on Sunday afternoon.
Southgate still has plenty to ponder before then, with fitness concerns remaining over Manchester United skipper Harry Maguire and Liverpool captain Jordan Henderson.
Southgate was also unable to call upon the seven members of his squad who featured in the Champions League final and will run the rule over Ben Chilwell, Reece James, Mason Mount, Kyle Walker, John Stones, Phil Foden and Raheem Sterling in the coming days.