The former captain missed England's dramatic one-wicket win in the third Test at Headingley after being felled by a bouncer from paceman Jofra Archer in the drawn second match of the series at Lord's.
Stuart Broad took two early wickets, including David Warner for a duck.
Steve Smith, who suffered concussion after being hit on the head by Jofra Archer in the second Test at Lord's, returns after sitting out last week's agonising loss at Headingley
Waugh has held similar mentoring positions with other sporting teams, including Australia's Olympic team for the 2008 Games in Beijing and 2012 in London.
A full 28 years after Botham's iconic 149, Stokes' unbeaten knock secured England an unlikely one-wicket win in the third Test and in the process kept the Ashes alive by levelling the series.
The sight of Leach carefully polishing his glasses as England closed on their record fourth-innings winning total also endeared him to the crowd.
Australia currently lead the series 1-0 with the second game at Lord's ending in a draw. The visitors had won the first Test by 251 runs in Birmingham.
Light rain from grey skies saw both the pitch and square remain covered for what was the first Ashes Test at Yorkshire's headquarters for a decade.
Barbados-born Jofra Archer had one of the most memorable Test debuts in recent times during the second Ashes Test between England and Australia at Lord's.
Some of the major talking points ahead of what promises to be an intriguing encounter.
Star Aussie batsman Steve Smith has been ruled out the third Test at Headingley after suffering a concussion in the second Test at Lord's.
Archer, who made his Test debut in the second match at Lord's which ended in a tense draw, returned match figures of 5/91.
Labuschagne came into the Australia team on the fifth day of the second Test against England at Lord's after Steve Smith was diagnosed with a delayed concussion.
Surrey left-arm seamer Sam Curran, who did not play at Lord's, retained his place in a 12-man squad for the third Test, which starts at England captain Joe Root's Headingley home ground on Thursday.
Similarities have since been noted between the blow that Smith received and the one that the late Phillip Hughes got in a domestic game in Australia which eventually led to his death in 2014.