Woods, who ended an 11-year major title drought last month at Augusta National, and Koepka, who held off Woods to win last year's PGA crown, join reigning British Open champion Francesco Molinari of Italy in the feature group of the first two days.
"I'm just looking forward to playing with him," Koepka said of Woods. "I don't think we've really been paired together too much, especially over the last couple years. It'll definitely be interesting."
It's the same layout where Woods won the 2002 US Open and shared sixth behind winner Lucas Glover at a rain-hit 2009 US Open, both times with the vocal support of New York crowds who made the Long Island trek.
"This week is going to be a lot of fun with the crowds, the excitement that we've had here," Woods said. "The pairing I'm involved in, it's going to be just a boatload of fun for all of us."
Woods would match Sam Snead's career US PGA Tour win record of 82 with a triumph and move within two of the all-time major win mark of 18 by Jack Nicklaus with a victory.
The 43-year-old American would become the 10th oldest major winner, two days older than Ted Ray when he won the 1920 US Open, and match record co-holders Nicklaus and Walter Hagen with a fifth Wanamaker Trophy.
He would also be halfway to a calendar year Grand Slam, the PGA shifting to May for the first time since 1949 in a revamped world golf calendar.
Woods won the first two majors of 2002 at the Masters and US Open at Bethpage, where two inches of rain has soaked the course.
"In order to win this one, driving is going to be at the forefront with the rough as lush as it is," Woods said. "Fairways are plenty wide because it's wet. You've got to hit it not only straight but you've got to hit it far."
Woods played a practice round last week but will have only two nine-hole sessions this week ahead of what could be an endurance test over the 7,459-yard, par-70 layout.
"This is not only a big course, but this is going to be a long week the way the golf course is set up. This could be a hell of a championship," Woods said.
"There's definitely going to be a component to stamina as the week goes on. Four days over a tough championship that is mentally and physically taxing takes its toll."
- Koepka, McIlroy go long -
Koepka could become the first golfer to own back-to-back titles in two different majors at once, having defended his US Open crown last June at nearby Shinnecock before denying Woods last August at Bellerive.
"I've got good memories," Koepka said. "It's a fun place to play in front of the fans. They're all energetic and hopefully you ride that momentum."
Koepka will hope to take advantage of wet conditions as well.
"Being wet will make those fairways a little bit wider and these greens will be quite receptive," he said. "If you can't find the fairway here, I don't think you're going to be able to go for the greens.
"I think you've got to attack the par-5s. with my length, you've got to take advantage of the par-5s and just try to hang on on the rest of them."
Woods and Koepka join fourth-ranked four-time major winner Rory McIlroy of Northern Ireland and England's second-ranked Justin Rose with a chance to overtake American Dustin Johnson for the world number one ranking this week with a victory.
"It's a long golf course and it plays even longer with the cold and wet conditions," McIlroy said. "Length is definitely going to be a big factor this week.
"You have to hit the ball in the fairway. That's a big stat, driving accuracy. If you start to miss these fairways you're not going to be able to get to the greens."
- Intimidating Bethpage -
Bethpage Black surrendered only six sub-par scores in hosting two prior majors.
"You lose a shot or two out there, and you don't feel like you're going to get it back. That's the intimidation factor of Bethpage Black," Ireland's Padraig Harrington said. "Bethpage, it really doesn't give you anything."
New York fans will give you delight or misery, as when they taunted a waggle-prone Sergio Garcia in 2002.
"Players want to have a buzz," Harrington said. "New York crowds for me are great. I do like a little bit of boisterousness."
"I think they're planning on letting 60,000 in a day here this week," McIlroy said. "So it'll be pretty loud."