Johnson, at 7-1, is the favorite at the Caesars sportsbook, followed by Koepka, Woods and Rory McIlroy, who were each 9-1 on Wednesday morning.
At Caesars, more money had been wagered on Koepka, the winner of the past two U.S. Opens, than any other golfer, but Johnson and Woods were not far behind.
"The top three are very close in money," Jeff Davis, head of risk management for Caesars sportsbook, told ESPN. "Distant from [Jordan] Spieth in fourth."
The money bet on Koepka and Woods accounted for 26 percent of the entire amount wagered in the U.S. Open pool at DraftKings sportsbook.
Woods won the Masters in April, but he missed the cut at the PGA Championship in May. He is the only player in the past 30 years with a career scoring average under 70 in majors held at Pebble Beach.
On Wednesday at MGM sportsbooks, Woods was listed as the favorite to win the U.S. Open. The SuperBook at Westgate Las Vegas reported taking a $10,000 bet on Woods to win this week, the largest the bookmaker had taken on its odds to win the U.S. Open.
Spieth (16-1), Patrick Cantlay (18-1) and Phil Mickelson (20-1) are in the next tier of contenders on odds boards. Bookmaker William Hill U.S. reported taking a $10,000 bet on Spieth at 14-1 on June 5. The bet would pay a net $140,000.
Mickelson needs a win at the U.S. Open to complete the career grand slam. A bettor at the SuperBook placed a $44,000 bet that Mickelson will not finish in the top 5, according to executive director John Murray. The bet would net $4,000 if Mickelson finishes outside of the top 5.
Players are expecting a typically rugged course setup at the Pebble Beach, where par is 71. The over/under on the winning score at Caesars is 277.5, 6.5 under par.