Stewart, who has been married twice before, said: "I left it this long because I wanted to get it right this time. I've never been happier and more in love than I am today."
The magazine said Stewart popped the question to the lingerie model atop the Eiffel Tower in Paris.
"I was stunned, threw my arms around him and burst into tears," Lancaster said. "I opened the box and he had bought me the most amazing princess cut diamond engagement ring."
"There are no wedding plans yet," said Lancaster's agent, Nicholas Young. "Rod's preference is to get married in Scotland if possible. He asked her father's permission first and, having been satisfied his intentions were honorable and his prospects were reasonable, he gave consent."
Celebrity Families of 2014 [PHOTOS]