The couple - who met on the set of 'The Rum Diary' - are officially back together after a brief split and are thought to have moved in together again, with a view to getting married in the future.
The 49-year-old actor has been dating Amber on and off since he separated from his long-term partner, Vanessa Paradis, in June 2012, and forked out on a $16 million ranch in Nashville, Tennessee, in December as a love nest for his new girlfriend.
A source told The Sun newspaper: ''Johnny's told Amber he wants to marry her and have children after introducing her to his kids [by Vanessa] Lily Rose and Jack.
''He's bought her another horse [for the ranch] so the one he got her last year can breed.''
It was reported that bisexual Amber had dumped Johnny in January because she was tired of his moods, but the 'Pirates of the Caribbean' star won her back by showering her with expensive gifts.
The 27-year-old blonde - who was spotted with Johnny at a Rolling Stones concert in Los Angeles over the weekend -is determined to give the relationship another go and is hoping to spend more time with his children.
The insider added: ''She's smitten with him but won't take any nonsense. She wants him to calm the late nights and whisky drinking before they plan a wedding.
''They're going to stay with the kids at his house in Plan de la Tour in the south of France, so it's full steam ahead again.''