Smith, who played six Tests for Australia in 1987 and nine for Ireland after switching allegiance, had battled cancer.
Once described by former Wallabies coach Alan Jones as one of the world's most gifted players, Smith was most recently the Head of Sport at Scots College in Sydney, where Bell and many other Wallabies graduated from.
"He was coaching at the Scots school and coached a lot of us coming through the grades and I just wanted to say it's a really sad time," Bell said from Wallabies camp in Townsville on Wednesday.
"We're wishing the best for his his wife and kids. He's an avid rugby person and helped a lot of individuals in the squad and in the Wallabies today, so just sending my condolences from the Wallabies and both myself."
Smith, who also played 43 games for Balmain and Eastern Suburbs from 1991 to 1994, coached Bell at GPS and NSW schoolboys' level when the emerging front-rower was only 16.
"Fair to say that I wouldn't have played as good or anywhere near as good without him," Bell said.
"Me, Jeremy Williams and Will Harris from the (Western) Force were really close with him and he was a great bloke, a great father and a great coach.
"So, yeah, very sad."
After playing schoolboys' rugby for Australia, Smith made his Wallabies debut under Jones in 1987, partnering Nick Farr-Jones in the halves and bagging 18 points from a try, five conversions and a penalty in a 65-18 win over South Korea.
Post-playing, Smith coached in Japan and England, where he was the national team's attack coach, and served as Australia's sevens coach.
"Brian had been very unwell in recent months and was battling an aggressive cancer," Scots College principal Dr Ian PM Lambert wrote to school colleagues.
"This is very sad news for our College community and I know it will come as a shock to many of you who knew and worked closely with him.
"Our immediate thoughts are with Brian's wife Lisa, his daughters Ruby and Santana, and his son Chilli."
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