Stephen Flynn was chosen by the party's group at Westminster earlier this week after his predecessor Ian Blackford stepped down from the role he held since 2017.
Mr Flynn, the MP for Aberdeen South, recently denied allegations he plotted to oust Mr Blackford.
Alison Thewliss, who ran against Mr Flynn in the leadership contest, has been given the home affairs role, while Stuart McDonald, who ran alongside her, was given justice and immigration.
Stewart Hosie has been appointed to the economy spokesman post, while David Linden will take on the social justice brief.
David Doogan has taken over the position of defence spokesman and Chris Stephens has joined the front benches in the levelling up position.
The reshuffle follows the announcement from SNP MPs Chris Law, Pete Wishart and Stewart McDonald that they were stepping down to go to the back benches.
In his resignation letter, Mr Wishart said he was "bemused" that Mr Flynn felt a change of leadership was necessary.
Announcing his new front bench, Mr Flynn said his group were willing to take the "independence momentum" to Westminster.
He said: "The Westminster group are on the front foot and ready to harness that momentum, and are entirely focused on standing up for Scotland's interests and our democratic right to decide our future.
"We have a new dynamic front bench team and within the whole group we have a wealth of talent, experience and expertise.
"We are in the best position to hold Westminster to account and support our Scottish Government and Holyrood colleagues in delivering independence for Scotland."
A new role on EU accession has been launched, with Alyn Smith taking up the post which will tackle the impacts of leaving the EU.
Mr Flynn added: "I would also like to welcome those who are new to the front bench, congratulate those with new positions and thank the whole team for their continued, tireless work.
"With the Tories and Labour both backing Brexit and denying democracy by standing in the way of a Scottish independence referendum, only the SNP is truly standing up for the people of Scotland.
"Support for independence is growing because people know that it is the only route back to the EU, and the only way to escape the broken Westminster system. The SNP Westminster team will work hard to make it happen."
And he told BBC's Drivetime programme on Friday that he did not plot to become the new leader amid rumours of a coup within the group.
He said: "Of course not.
"I think what we've seen over the course of recent days and recent weeks is that some folk have been watching a little bit too much House of Cards.
"There's been some very uninformed opinion in the public domain."
And in response to Mr Wishart's letter, he said: "Ian himself took the decision to stand down and it's for Ian to address any concerns that Pete might have in relation to that.
"I can't speak for Ian in that regard."