Under the "restructuring" plans the firm would be 89 per cent-owned by the US government and the United Auto Workers (UAW) union, as long as both workers and officials approve the plans.
GM shares rose 34 cents, or 20.7 per cent, to $2.03 in morning trading on Monday, while US stocks rose slightly in midmorning trading, with the Dow Jones Industrial Average rising 15.37, or 0.2 per cent, to 8,091.56 points.
Following criticism from the administration of Barack Obama, the US president, GM said it would reduce the number of US plants to 34 from 47 by the end of 2010, slash the US hourly workforce by about 21,000 to 40,000 and cut its dealer network to 3,605 from 6,246 stores.
The company said it would also phase out its Pontiac brand, one of the US's most famous models, no later than next year.
Its Hummer, Saturn and Saab brands may also either be sold or phased out.
The Obama administration's "autos task force", which has been overseeing GM's planning for the past month, said the steps showed the carmaker was making some progress.
The task force, headed by Steve Rattner, a former investment banker, welcomed GM's plan to swap bonds for shares, saying in a statement that: "[This] bond exchange filing represents an important step in GM's effort to restructure".
Fritz Henderson, GM's chief executive, said on Monday he expects to break even in the US auto market, with annual sales of almost 10 million units after the cuts.
This would permit the firm to begin generating cash as soon as next year if the US market sees a modest recovery, Henderson said.
Previous plans submitted by GM to the Obama administration were rejected as too small scale and too slow when Rick Wagoner, the firm's former chief executive, was ousted last month.
GM, along with fellow car giants Chrysler and Ford, has faced heavy criticism for failing to restructure its businesses amid sales slumps and a looming recession, and for not responding to market demand for more fuel-efficient vehicles.
GM and Chrysler received a combined $17.4bn in emergency loans approved in December, but further requests this March were rejected after Obama said their restructuring plans did not go far enough.
Ford has said it has enough money to survive the downturn without government aid.