updated 03/18/2014 AT 1:00 PM ET
•originally published 03/18/2014 AT 2:15 PM ET
A safari with George Clooney? That’s one trip to remember.
The Monuments Men actor whisked his new girlfriend, British lawyer Amal Alamuddin, off for a jaunt to Tanzania to watch wildlife.
Exclusive photos in the new issue of PEOPLE show the couple on one of their first trips together after romance rumors swirled when they were spotted dining together back in October.
Clooney and Alamuddin have also been spotted vacationing together in the Seychelles.
The couple recently turned up together for a special screening of Clooney’s latest movie on Feb. 18 at the White House alongside President Obama.
When they had a nightcap at a local hotel afterward, “his arm was around her shoulder and she had hers around his,” an observer told PEOPLE at the time. “They just seemed very, very together.”
“He’s with someone who is a very accomplished attorney. She isn’t someone who is pursuing a career in acting or entertainment,” says the source. “She’s on his level.”