"Welcome home little buddy," Woolard, 33, captioned his own post, on which Brown commented: "So glad you're my doggie's daddy."
She previously shared a glimpse at their first time meeting the Australian labradoodle at the airport on her Instagram Story. "Well... I'm an official dog mom," Brown wrote.
Brown posted a video of Wally's first car ride, which was followed by his first walk on a leash, his first trip to the beach, and his first time successfully going to the bathroom this weekend. She even took a poll among her 2.5 million Instagram followers on whether she should start his own profile.
The Dancing with the Stars alum later offered a recap of Wally's first day. "First day with Wally has been so much better than I even expected. He's so awesome. ... He's been super tired today but also really fun. He's fun to play with. ... He's calm but still playful," she shared.
"He's just the best little dude. Best boy. ... I know it's the first day but he's checked off all the boxes. He pooped on his poop pad!" Woolard added, as Brown chimed in: "First time. First poo on the poop pad. Now, we did chase him with it and maybe put it under there, but he did it."
Wally also received some love in the comments section. "Adorable!!!!" Andi Dorfman commented. "Welcome to the dog mom club babe!" Sailor Brinkley Cook wrote, while Matt James responded with screaming emojis.
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"I've always longed for safety in relationships but I've put myself in unsafe positions," Brown said in November. "Adam keeps showing up. And he always makes me feel so safe."