Stewart bought a $2.1 million home just a mile and a half from Pattinson's Los Feliz house, according to real estate site Zillow.com.
Meanwhile, the newly reunited couple have been spending lots of time together privately and publicly.
"They seem attached to the hip again," one observer tells PEOPLE. "They spent all weekend together. They are back to hanging out with their old group of friends. Everything seems back to normal again."
On Saturday, Stewart, 22, and Pattinson, 26, arrived hand-in-hand for a late night dinner date at Chateau Marmont in West Hollywood. On Sunday, they spent a fun-filled night out with friends at the Ye Rustic Inn, near Pattinson's Los Feliz home.
"Rob and Kristen sat next to each other all night," a witness at the Ye Rustic Inn tells PEOPLE. "They were both in a great mood. They kept smiling at each other and were laughing with their friends. They looked happy and everything seemed great. They were flirty and held hands, but didn't kiss."
On Monday, the couple also had lunch out together in Hollywood.
The couple will make their first official appearance together later this month to promote The Twilight Saga: Breaking Dawn – Part 2.