Ms Swinson, who took back her seat after losing it two years ago, was the bookies’ favourite and had the greatest support among Lib Dem members, according to a party survey.
Her decision clears the way for Vince Cable or Norman Lamb to seek the party leadership, following Tim Farron’s decision to stand down following controversy over his religious views.
Ms Swinson, a former business minister in the coalition government, said the deputy leadership was “the right role for me now”.
“I have been overwhelmed by so many lovely messages from people I know, and from many members I have not yet met, encouraging me to stand for leader,” she said. “Being the leader of a political party is a unique and all-encompassing job, even more than the roles of MP and minister that I have undertaken before. It should not be done simply to achieve status, to make a point, or to please others.
“Feminist that I am, I have of course wondered what a bloke in my position would do... It’s true that my many years of encouraging women to have the confidence to go for that exciting new role have taught me that women often don’t go for things when they should.
“But just as often I have observed men going for the promotion when they shouldn’t. Just because a man would do it, doesn’t make it the right thing to do. I have consistently fought against stereotypes and structures that impose a choice on someone, rather than allowing them to make up their own mind.”
Ms Swinson could still end up running the party on an interim basis after Mr Farron steps down in July, if she is successful.