The former Dudley North MP said the report marked "a shameful day for Labour and a vindication of those who bravely spoke out about the poison of anti-Semitism that spread under Jeremy Corbyn's toxic leadership".
Mr Corbyn was suspended following the publication of the report by the Equality and Human Rights Commission (EHRC), which said Labour was responsible for unlawful acts of harassment and discrimination during his time as leader.
The watchdog also said it found evidence of "political interference" by his office in the complaints process, and pointed to "inexcusable" failures which "appeared to be a result of a lack of willingness to tackle anti-Semitism rather than an inability to do so".
Mr Corbyn has refused to accept all of the EHRC's findings and vowed to "strongly contest" his suspension.
Lord Austin quit Labour in February last year, blaming its lurch towards extremism under Mr Corbyn.
He told the Express & Star: "The EHRC's watershed report should mark the end of a chilling chapter in Labour’s history and signal the beginning of a new era where trust is rebuilt and extremism is driven from the party.
"Yet the scale of that challenge has been laid bare by Labour's suspension of Corbyn, who still insists Labour's anti-Semitism problem was "dramatically overstated for political reasons".
"Keir Starmer has made a good start – issuing a profound apology for the past, promising wholesale culture change and a 'zero tolerance' approach to anti-Semitism.
"He was right to suspend Corbyn but faces a huge challenge to clean up the party, introduce a robust new complaints process, purge the party of the extremists and rebuild trust with the British Jewish community.
"From now on, actions will matter more than words."
A spokesman for the Labour Party confirmed Mr Corbyn had been suspended and had the whip withdrawn.
Walsall South MP Valerie Vaz, the Shadow Leader of the House who served in Mr Corbyn's frontbench, said: "I agree with the leader Keir Starmer's position that the EHRC report and recommendations are accepted in full.
"For those who do not this is a matter for the General Secretary of the Labour Party and due process will be followed."