The Cesar 911 star is engaged to longtime girlfriend Jahira Dar, he announced on Instagram Monday morning, before sharing details of his proposal exclusively with PEOPLE.
"After six amazing years together, I am so happy I asked her to be my wife. Thankfully, she said 'yes'!" Millan, 46, tells PEOPLE. "My pack is complete!"
"Jahira came into my life at just the right time. She was instrumental in helping me rebuild my life and my family after my divorce and break from the Dog Whisperer television show," Millan says. "She is compassionate, gentle, instinctual, spiritual, intelligent, fun, strong, adventurous, and loving.
"She embodies the principles that I prize the most – honesty, integrity and loyalty. On top of all of that, she loves dogs and mother nature just as much as I do."
Millan's March 24 proposal was the end of an elaborate surprise, a source tells PEOPLE.
Dar, an actress and former stylist and wardrobe consultant, and Millan were vacationing in Spain and Dar assumed they were headed for Italy, the source says – when Millan changed their tickets for Greece.
They had dinner at the top of Mount Lycabettus, in Athens; and Millan popped the question as the couple overlooked the Acropolis, with a violinist playing behind them.
"I wanted the proposal to be special and to surprise her, so I spent months planning our trip to Greece," Millan says. "I am still proud of myself that I never gave it away!"