Dawn Butler, the new shadow minister for diverse communities, told the BBC she felt it was a unifying reshuffle – amid criticism from some Labour MPs.
She said bringing in “formidable” Nick Brown as chief whip showed he was “not scared” of promoting someone who was not one of his natural supporters.
The sacking of Dame Rosie Winterton from the role disappointed some MPs.
Mr Corbyn, who was hit by a wave of front bench resignations and a no-confidence vote from the majority of his own MPs in the wake of the EU referendum result, was re-elected with an increased mandate from the wider party membership last month.
Labour reshuffle: Diane Abbott made home secretary
Some roles had remained unfilled in the interim.
New appointments announced on Thursday include Diane Abbott, who has been promoted from shadow health to shadow home secretary, former Liberty director Baroness Chakrabarti, who becomes shadow attorney general, and former director of public prosecutions Sir Keir Starmer, who left the frontbench team in June, as shadow Brexit secretary.
The decision to sack Dame Rosie Winterton – who was brought in to replace Nick Brown as Labour chief whip in 2010 – was met with a rush of tributes to her by senior figures including former leader Ed Miliband and former deputy leader Harriet Harman.
Neil Coyle MP tweeted: “There were plenty of spaces to fill in shadow cabinet if Nick Brown wanted one. Sacking unifying chief whip shows ‘reaching out’ meant nothing.” His colleague Tom Blenkinsop accused Mr Corbyn of “seeking submission not unity”.
BBC political correspondent Iain Watson said many Labour MPs had expressed disappointment that she had gone. One senior figure told the BBC the reshuffle was “vengeful and cack-handed”. Dame Rosie was seen as someone, behind the scenes, who stood up for MPs’ interests against the party leader, he added.
But Ms Butler, who supported Andy Burnham’s Labour leadership bid in 2015, against Mr Corbyn, said she believed Mr Corbyn’s reshuffle was an attempt at unifying the party.
“Jeremy has shown that he is a leader,” she said and was “making sure we have a full shadow cabinet to take on the government on Monday”.
She said Nick Brown’s return, having served under Tony Blair and Gordon Brown, showed “that Jeremy isn’t scared of putting someone in a position who doesn’t really support him but will do an excellent job as a chief whip”.
Jo Stevens, who has been brought in as the new shadow Welsh secretary, told BBC Radio 4’s Today programme agreed with Ms Butler that Mr Corbyn had reached out to unify the party.
“I was one of the senior people in Owen Smith’s leadership campaign and he’s offered me a place on the shadow cabinet,” she said.
“The Labour Party is a collective and we’re there to hold the government to account,” she added. “That’s why I stayed in my post in the summer and accepted the job.”
Ms Stevens said there would be opportunities on “plenty of issues” to unite the party against the Conservatives.
But the decision to promote Baroness Chakrabarti, who became a Labour peer shortly after holding an inquiry into anti-Semitism in the Labour Party and concluding that it was “not overrun” by racism, was met with some criticism from Jewish groups.
Board of Deputies Vice President Marie van der Zyl said: “We are disappointed, but sadly unsurprised, that once again Shami Chakrabarti and Jeremy Corbyn have spectacularly undermined her so-called ‘independent’ report. We hoped her report would be a potent weapon in the fight against anti-Semitism. It now looks increasingly like the whitewash was a job application.”
Mr Starmer stood down from his shadow home office minister post in June. He will now join shadow foreign secretary Emily Thornberry, shadow international trade secretary Barry Gardiner, new shadow economic secretary Jonathan Reynolds and shadow chancellor John McDonnell on Labour’s “shadow Brexit team”.
Sarah Champion has been made shadow women and equalities minister.