Chief executive Martin Slumbers said the move was because the US dollar is the "most widely adopted currency for prize money in golf".
The 2017 event begins on 20 July and the winner will pick up $1.85m (£1.4m) from a prize pool of $10.25m (£7.9m).
In February, the R&A told BBC Sport that the fall in sterling's value, which followed the vote to leave the European Union in June 2016, had made a "significant impact" in driving the proposal to pay Open prize money in American currency.
However, although the pound's value dropped after the Brexit vote, it has strengthened against the dollar since 1 January. A pound bought $1.29191 on 4 July, compared with $1.23458 on the first day of 2017.
That means that if a British player wins the event and converts his winnings back into sterling, it will actually be worth around £60,000 less than it would have at the turn of the year.