Norbert Roettgen also says the seven oldest reactors taken off the grid pending safety inspections following Japan's Fukushima nuclear disaster in March will remain offline permanently.
He says all but the three newest reactors will be shut down by 2021, and the remainder a year later.
Roettgen announced the agreement early Monday morning after hour-long negotiations between the governing parties.
Merkel in 2010 had pushed through to extend the lifespan of the country's 17 reactors with the last one scheduled to go offline in 2036, but she completely reversed her policy in the wake of Japan's nuclear disaster.