The former Labour prime minister praised his left-wing successor's policy priorities and growing popularity with the public, adding: “Jeremy is a phenomenon”.
Mr Corbyn was successfully tapping into rising public anger over the unfair effects of globalisation, after centrists appeared to show they had “no answers”, Mr Brown said.
“People feel rightly or wrongly that the problems that they have – stagnant wages, inequality, polarisation between rich and poor, public service not being properly financed - they ascribe that to the failures of governments, centrist governments that have not been able to manage globalisation,” he said.
On Mr Corbyn’s shock rise, Mr Brown said: “He has come through because he expresses people’s anger at what’s happened – the discontent.
“When he attacks universal credit, he is speaking for many people, when he says the health service is underfunded, he is speaking for many people.”
The Labour leader still had to show he had “a plan for the future that is credible and, therefore, a programme that is electable”.
“That’s the challenge for any left-wing or progressive party,” Mr Brown told BBC Radio 4’s Today programme.
He also expressed confidence in John McDonnell, the Shadow Chancellor – and bête noire of many moderate Labour MPs – noting he had backed Bank of England independence.
The endorsement is in stark contrast to Tony Blair’s warning that Mr Corbyn’s policies would be a disaster for the country.
Mr Blair has called for a return of centre-ground politics, once warning Mr Corbyn’s “populist policy making” would be a “very dangerous experiment for a major western country”.
In the interview, Mr Brown denied he was moving to the left, but argued Mr Corbyn’s success was because New Labour “did not finish the job” of curbing inequality and bad banking practices.
He had “articulated a view of a fairer society” by pinching the “for the many not the few” slogan first used by the Blair government, he noted.
The intervention comes after Nick Boles, a former Conservative minister, broke ranks to call for an end to “austerity” in this month’s Budget.
The David Cameron ally broke ranks by urging the Chancellor to rip up seven years of Tory economic policy, abandoning the flagship target to wipe out the Budget deficit.
And he sided with Labour by arguing that higher investment spending was needed to “generate a return to the economy” and end Britain’s productivity crisis.