The MP for East Renfrewshire, who won the constituency back from the Tories last year after holding it from 2015-17, follows Kirsty Blackman, who stood down citing the impact of the coronavirus lockdown on her mental health.
"I'm delighted to have been elected SNP Westminster Deputy Leader at this critical time, and I look forward to working in this new role with our strong team of SNP MPs,” Ms Oswald said.
"As we continue to tackle coronavirus, SNP MPs will press the UK government to deliver the financial powers and support that people, public services and businesses in Scotland need to manage this unprecedented emergency and secure a strong recovery.
"This crisis has exposed the deep inequality caused by decades of Westminster cuts. There can be no return to business as normal. As Scotland seeks to build a fairer society and escape the growing threat of a Tory Brexit, the case for independence has never been stronger."
SNP Westminster Leader Ian Blackford MP congratulated Ms Oswald and said she “brings a wealth of talent and experience to the role”.
"This is an important time as we deal with the covid-19 crisis and look to build a fairer Scotland,” Mr Blackford said.
“With the threat of a Tory Brexit growing, and crucial decisions over the economic emergency, Kirsten will play a key role as we hold the Tory government to account."
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