Doohan, dubbed the 'Becker Wrecker' after defeating two- time defending champion Becker at Wimbledon in 1987, passed away from motor neurone disease diagnosed just nine weeks ago.
Doohan reached a career-high world ranking of 43 and won five titles.
"Peter was unbeaten in Davis Cup representation. He won the South Australian Open singles title and reached No.15 in doubles," TA said in a statement.
"Following his retirement, Peter coached in the United States, after first studying at the University of Arkansas, where he was all-American and a NCAA champion. He returned to live in Australia in 2009."
"My heartfelt condolences to the family of #PeterDoohan! The tennis fraternity lost a great guy and wonderful player," Becker said on social media.
"RIP mate! You were the better player."
TA said the tennis community rallied around Doohan with a number of fund raisers during his battle with a particularly aggressive form of motor neurone disease.
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