Woods broke the news Friday.
"After a good recovery week I'm committing to play in the @ValsparChamp and @APinv next two weeks," Woods tweeted.
The 42-year-old golfer is ranked No. 389, up from No. 544 last week, according to the Official World Golf Rankings. He finished 12th at the Honda Classic on Feb. 25 at PGA National Golf Club in Palm Beach Gardens, Fla. Justin Thomas won the tournament after a one-hole playoff against Luke List. Woods shot an even-par 280 for the tournament.
Woods' appearance at the Honda Classic marked the first time since 2015 that he played in back-to-back events on the PGA Tour.
The Valspar Championship runs from Thursday, March 8 through Sunday, March 11 on the Copperhead Couse at Innisbrook Resort and Golf Club in Palm Harbor, Fla. The Arnold Palmer Invitational is from March 15 through March 18 at the Bay Hill Club and Lodge in Orlando, Fla.
"I've been pretty patient with it. I've still got some work to do, but I'm very pleased with the way I've progressed, especially this week," Woods told reporters at last week's Honda Classic.
Woods also said he's still trying to understand what his body can do.
"It's not like it used to be," Woods said. "Those angles are gone. So I've had to make a little bit of adjustments here and there and I think I've done that."
Woods' third round 69 at the Honda Classic was the first time he hit under 70 in an official round since 2015. The 14-time major championship winner carded a 68 in the third round of the 2015 Wyndham Championship.