Marsh, 31, will join the original 12-man squad in Adelaide, where the rescheduled four-Test series begins against India on Tuesday.
Clarke and his grief-stricken teammates attended Phillip Hughes’ funeral on Wednesday and began assembling in Adelaide late Thursday for next week’s series opener.
It is not yet clear if any of the Australian squad will withdraw from the Test, with emotions still raw following Hughes’ freak death last week.
Hughes, who had played 26 Tests and was on the cusp of a recall, died from bleeding on the brain after being hit by a rising ball at the Sydney Cricket Ground during a domestic match on November 25.
Cricket Australia has reassured those selected that they can withdraw from the Test if they are having problems emotionally.
“We hope the boys can find the inner strength to play the game in the way Phillip would have wanted in Adelaide next week and that they can honour what he had done,” coach Darren Lehmann wrote in a column for The Australian on Thursday.
“It’s going to be hard and if somebody is struggling Michael (Clarke) and I understand. There is no pressure on them.
“We will look after them and we will help them get back to the place where they can play.”
Hughes and Marsh were the leading candidates to replace Clarke last month, when the 33-year-old skipper was set to be ruled out of the first Test while recovering from a third hamstring setback since August.
The two Test contenders had both been in action for their respective state sides on November 25.
Marsh brought up a century that day with three sixes off Victoria legspinner Fawad Ahmed at the Melbourne Cricket Ground, but like all cricketers was later in a state of shock after hearing that Hughes had been rushed to hospital for emergency brain surgery. Hughes died two days later.
Shaun Marsh joined his brother, Mitch, in the squad and are one step closer to playing together in a Test match.
Shaun and Mitch, sons of 50-Test batsman Geoff, could become the first brothers to play in an Australian Test side since Mark and Steve Waugh in 2002.
“It would be huge,” Shaun Marsh said last month. “From a young age, we’ve both wanted to play Test cricket.”
Mitch will play his first Test at home next week, having made an impressive debut against Pakistan in October.
Shaun’s greatest Test knocks have all come overseas. In Australia he has amassed 17 runs from six innings, all against India in 2011-12.
India began a hastily rearranged two-day game against a Cricket Australia XI in Adelaide on Thursday to get in match practice ahead of the opening Test. -AFP