The pair will meet for the seventh time in their careers after the former British and world number one received a wildcard for the ATP 250 event, the final warm-up tournament before the US Open, which starts on August 30.
Murray leads the individual head-to-head 5-1 with Kyrgios' only win coming in their most recent match three years ago at Queen’s Club, where the Scot made his return following his first hip surgery.
The two are friends off the court, with Murray describing the Australian as one of the most entertaining players to watch, so long as his head is in the game.
"I like watching [Nick] Kyrgios when he’s into it,” he said. “When he’s not into it, I don’t enjoy that at all. But when he’s into it, I really enjoy watching him."
Murray is coming off the back of a second round exit at the Cincinnati Masters, where he pushed Wimbledon semi-finalist Hubert Hurkacz in a tight two-setter in the second round following a straight sets win over Richard Gasquet in round one.
Kyrgios, meanwhile, will be taking part in his fifth tournament of the year outside Australia, having retired from Wimbledon with an injury in the third round, before playing in the North American hard court swing.
The first round match takes place on Monday with winner due to play 13th seed Frances Tiafoe in the second round.