The 40-year-old comedian and Laura — 27 — who is five months pregnant, are set to welcome their first child into the world, reports dailymail.co.uk.
A source told The Sun newspaper: “Russell might have bedded many of the world’s most stunning women but now it’s all about Laura and becoming a dad.
“They have been living as a couple for the last six months and are determined to make a go of their relationship. It feels like a new chapter in their lives and the couple are enjoying every moment, including discussing baby names”.
Brand and Gallacher are said to be making plans for a nursery at their luxury riverside home in the village of Aston near Henley-on-Thames, Oxfordshire.
Among his list of previous high-profile girlfriends are Kate Moss, Courtney Love, former Spice Girl Geri Halliwell and Jemima Goldsmith.
Brand married singer Katy Perry in 2010, but they divorced two years later. Laura – the younger sister of TV presenter Kirsty Gallacher, first began dating Brand in 2006 and they have been in an on-off relationship since then.