Steinbrück, 65, was one of three potential leaders considered by the centre-left Social Democratic Party (SPD), which had been expected to reach a decision by the end of the year. He served as finance minister under Merkel in the “grand coalition” between the SPD and her Christian Democratic Union.
"I accept this challenge in order to win the next federal elections, with and for the SPD," Steinbrück told a news conference.
"That is the demand, that is the ambition. We want to remove this government. It's obvious that this government will not be returned in a year.
"But we don't just want it to be partly replaced, we want it to be replace by a red-green government," he said, referring to a coalition between his SPD and the Green party.
The SPD leadership troika of Steinbrück, party leader Sigmar Gabriel and parliamentary party leader Frank-Walter Steinmeier, who failed to oust Merkel last time around, has become increasingly uneasy with each other, increasing calls for a clear decision.
On Friday Gabriel publicly nominated Steinbrück as chancellor candidate, while Steinmeier promised to fight for him “as if it were my own fight.”
The straight-talking style of the trained economist has ruffled feathers in the past, notably when he described the Swiss as "Indians" during a bitter tax row between the two neighbours.
He also sparked outrage in Britain when he dismissed London's economic policy as "crass" and "breathtaking."
Opinion polls show that he is considered the third-most significant politician in the country behind Merkel and current Finance Minister Wolfgang Schäuble but he has a lot of ground to make up if he is to become chancellor.
A poll conducted by public broadcaster ZDF – before the news broke of his candidacy – found the Social Democrat favoured by 36 percent of those surveyed, opposed to Merkel's 53 percent.
The focus of Germany's political pundits and media on the ascension of Steinbrück was good news for Kurt Beck, state premier of Rhineland Palatinate, who announced his resignation on Friday after 18 years in the job - following harsh criticism of his handling of the Nürburgring development.
The 63-year-old was expected to make a formal announcement on Friday evening after meeting with his state party leadership. He is expected to be replaced as state premier by Malu Dreyer – who would become the first woman to hold that post. She suffers from multiple sclerosis but has never made a secret of her desire to take on the state's top job.