Murray, the champion in 2009 and 2011, rallied to defeat fourth-seeded Frenchman Jo-Wilfried Tsonga 4-6, 6-3, 6-2 in a repeat of their 2011 final. Fifth-seeded Cilic of Croatia held off former four-time winner Lleyton Hewitt 6-4, 4-6, 6-2.
Murray will play for his 27th career title and first since he won in Miami in March.
Cilic had lost his only previous meeting with Hewitt, at the London Olympics. He will bid for his 10th career title. His last tournament victory came in February at home in Zagreb.
Tsonga held the upper hand over Murray in the opening set of their semifinal. He failed to convert any of his three break points at 2-2, but break to lead 5-4 when Murray double-faulted.
The Frenchman missed two more break points at 3-3 in the second set before Murray broke for a 5-3 lead when Tsonga netted a backhand.
In the last set, Murray broke for 2-1 on his seventh break point and broke again at love to lead 4-1.
"I think most of the matches there has been patches where I played a high level, and all the matches it's been parts where, you know, I have been a little bit inconsistent or just played a couple of sloppy games," Murray said.
"I managed to find ways to win the matches, which is important, and I'm playing well. I'm hitting the ball well. Just sometimes making some bad choices or some poor mistakes."
Cilic and Hewitt managed to complete just two games, with Cilic leading 2-0, before rain forced them off the grass court for more than 2 hours.
To finish both semifinals before dark, their match was moved to court one so the higher-ranked Murray and Tsonga could play on center court.
After play began, Hewitt held three break points to tie it 5-5, but Cilic held serve to win the set.
Hewitt swept five straight games on his way to taking the second set, before Cilic gave up just 10 points in winning the last five games of the match.