Smith, who had one year left on his deal with the Chiefs, will reportedly be tied to the Redskins for five seasons in total.
He'll earn $23.5 million per season over the four-year extension, including about $70 million in guarantees, according to Chris Mortensen of ESPN.
The 33-year-old is coming off his second consecutive Pro Bowl season after posting career highs in passing yards (4,042) and touchdowns (26) in 2017, while throwing only five interceptions. He made three Pro Bowls in five years with the Chiefs, but was never able to push Kansas City past the divisional round of the playoffs.
Smith provides the Redskins with stability at the most important position on the field after they failed repeatedly to strike a long-term deal with Kirk Cousins. Cousins is set to hit free agency in March after playing the last two years under the cloud of the franchise tag.