But he started a mere seven of the final 19 Premier League appearances of his United career, with Rooney no longer a first-choice player under manager Jose Mourinho.
"The players are very keen that Wayne wears the number 10 and we believe that is a fitting tribute", Southgate told a news conference on Wednesday.
City midfielder Delph confirmed that he would hand the armband over to Rooney when he makes his 120th and final global appearance.
Manchester City player Delph said: "When I first came into the England set-up, Wayne was captain".
"Obviously some players I have played with, some players I haven't but it was nice to see all the players and the staff and the reception they gave me was fantastic, so it's great to be back".
Rooney retired from global duty with 53 goals in 119 games for the Three Lions, meaning not only is he England's all time leading goal scorer, but he's his country's second most capped player, behind Peter Shilton, who earned 125 caps during his career.
Oil struggles to find footing after 7% fall
The Organization of the Petroleum Exporting Countries (OPEC) has been watching the jump in supply and price slump with concern. Meanwhile, Saudi Arabia unveiled a plan over the weekend to reduce its shipments by about 500,000 barrels a day next month.
"He's the record holder with the number of goals he's scored for England and it's right for us to make a day for him and make it special".
Southgate did not want to fix a time in the game when Rooney would come on but said he had discussed it with the 33-year-old.
England face Croatia in a Nations League match on Sunday.
Southgate was saddened that Rooney had faced such questions. "We think it is important to honour him for the achievements he has made throughout his career". "The most important thing is that within the England group we value what he has done and what he has given", he said.
"There's no guarantee I will get on but I've still got probably 15 to 20 family members and friends coming to watch, which shows what they want for me and what I want for myself. I feel like I can score goals so I'm just hoping I can stay fit, in form and get some opportunities".
"I think we have put young players in no matter what the situation has been", he said. "Hopefully he has felt that warmth from all of us and I know the reaction of the supporters will be very special to him", added Southgate.