Woods is under par after the opening round of a major championship for the first time in five years. The last time Woods shot under par in the first round of a major came in the 2014 Open when he shot 69 at Hoylake.
Woods broke par at Augusta National for only the ninth time in 22 starts. He shot a 2-under-par 70 that put him in a tie for 11th place. He made four birdies and two bogeys, with the last coming at the par-4 17th hole.
The 43-year-old Woods has appeared in the Masters only three times since 2013 due to multiple back surgeries. He tied for 32nd in last year's event.
"I felt like I played well and did all the things I needed to do to post a good number," Woods told reporters. "I drove it well, hit some good irons and my speed was good on the greens. It was tricky. The wind puffs up, it goes down, it switches directions. It just kind of swirls out there, and it is hard to get a bead on exactly what it is doing at all times."
Several players with late tee times made runs later in the afternoon, including three-time major champion Koepka. He missed last year's Masters due to a wrist injury and has won three majors since he last competed at Augusta.
Koepka and DeChambeau made the turn at 1-under before speeding through the back nine of the course. Koepka and DeChambeau each shot a 6-under 66 to grab a share of the first-round lead.
Koepka played a bogey-free round and had birdies on five out of six holes on Nos. 10, 12, 13, 14 and 15. He could have moved to 7-under on the 18th hole, but his putt curved to the right.
DeChambeau ended his opening round with six birdies on the final seven holes. He had a bogey on the 14th hole.
The second round of the Masters continues Friday morning.