Fast bowler Mitchell Starc retained his place for Friday's match despite carrying a rib niggle and will line up in the attack alongside Pat Cummins, Scott Boland and Nathan Lyon.
"Mitchy obviously hasn't quite got the runs or wickets he would have liked this series and felt like it was time for a freshen up," said skipper Cummins.
"Beau's been with the squad and been great.
"It's a shame for Mitchy because we know how much he brings to the team, but we feel like now is a good time for Beau to get a chance."
Marsh's position had been under intense scrutiny after a poor series with bat and ball and his axing could potentially herald the end of the 33-year-old's Test career.
After making his debut in 2014, he struggled to cement his place in the team and with the emergence of Cameron Green had been on the red-ball sidelines in recent years.
He returned to the Test side when Green was ruled out of the series following surgery on his spine.
Cummins said Marsh, who remains a key figure for Australia in the white-ball game, took the news well.
"He was totally understanding. I think his words were, 'I'm not necessarily blindsided.'
"He knows he hasn't scored the runs or (taken) wickets he would have liked so that makes you vulnerable."
Tasmanian Webster, 31, has toiled for years in Sheffield Shield cricket and will be Australia's third debutant in the series.
Teenage opener Sam Konstas was called up for the fourth Test in Melbourne, in place of Nathan McSweeney who had made his debut in the first Test in Perth but had a poor run and was dumped after the third in Brisbane.
Konstas announced himself with a quickfire 60, audaciously ramping India's premier fast bowler Jasprit Bumrah for a six.
Webster can bowl pace and off-spin and was considered a better option in case left-armer quick Starc has any issues.
Starc bowled 41 overs in Melbourne -- which Australia won by 184 runs on day five -- but clearly struggled in the latter stages.
But despite this Cummins said: "He was never going to miss this one."
Australia are 2-1 up in the series and will regain the Border-Gavaskar trophy for the first time since 2014-15 if they win or draw the Test which begins on Friday.
Victory would also guarantee them a place in the June World Test Championship final at Lord's against South Africa.
Australia: Sam Konstas, Usman Khawaja, Marnus Labuschagne, Steve Smith, Travis Head, Beau Webster, Alex Carey, Pat Cummins (capt), Mitchell Starc, Nathan Lyon, Scott Boland
