Deposed Australia captain Steve Smith has returned home from time out overseas, saying he is prepared to win back trust after his role in a high-profile ball-tampering scandal.

Smith, who was sacked and sent home in disgrace after the third Test against South Africa, had been lying low in New York but made his first appearance on social media in a month to thank the cricket public for giving him a second chance and his family for their support.

The former skipper posted a Dani back in Sydney and said he wouldn't be taking his fight to earn back trust for granted.

"It's great to be back home in Australia. I have had some time away to come to terms with everything and now it's time to get back into it," Smith wrote on Instagram on Friday.

"The amount of emails and letters I have received has been incredible and I have

been extremely humbled by the enormous amount of support you have given me.

■ I now have a lot to do to earn back your trust."

Cricket Australia last month suspended Smith and team vice-captain David Warner from all international and domestic cricket for a year, while Cameron Bancroft was suspended for nine months.

Bancroft was caught by TV cameras trying to tamper with the ball using sandpaper, triggering a dramatic series of events that led to the banning of the three players and coach Darren Lehmann standing down from his role.

Smith was greeted back by Lehmann, who tweeted "welcome home mate" in response to the 28-year-old's post.

Former Test Justin Langer was Thursday appointed as Lehmann's successor in all three formats of the game.