The MP - who has been in the role for more than five years - has confirmed he will not be restanding for the position at the party's AGM next week.
He has said it is time for "fresh leadership" ahead of the next General Election.
Blackford has also revealed he has accepted a new role "at the centre of the SNP's independence campaign" leading on business management.
Aberdeen South MP Stephen Flynn has been touted as the frontrunner to replace Blackford.
In a statement, Blackford said: "I have today informed SNP MPs that I will not be restanding as leader of the Westminster parliamentary group at our AGM next week.
"After more than five years in the role, now is the right time for fresh leadership at Westminster as we head towards a general election and the next steps in winning Scotland’s independence."
During Blackford's time as SNP Westminster leader, the party won a landslide victory at the 2019 General Election with an increased share of the vote while securing more MPs.
The Ross, Skye and Lochaber MP added: "Support for independence has continued to grow with polling this week showing a majority in favour.
"While I am stepping down as Westminster leader, I will continue in my role as the MP for Ross, Skye and Lochaber, and I have also accepted a new role at the centre of the SNP’s independence campaign, leading on business engagement.
"I would like to thank our MPs and staff for all their support over the past five years. Whoever replaces me as Westminster leader will have my full support as, together, we stand up for Scotland's interests and democratic right to choose our future in an independence referendum."