New forms including “parent one” and “parent two” alongside “mother” and “father” are expected to be brought in by the end of the year.
The Home Office says the additional terms will ensure passports are issued safely to the right person.
Gay rights groups say the current form is “discriminatory” but family values campaigners say the changes denigrate the roles of mothers and fathers.
The proposals also include sex-free passports to allow transgender people to opt out of identifying themselves as either male or female.
Sam Dick, head of policy at gay rights group Stonewall said: “These changes simply reflect the realities of modern life for families – making it clearer for same-sex parents applying for passports for their children and more straightforward for the officials who process them.”
Norman Wells, director of the Family Education Trust, said: “To speak of ‘parent one’ and ‘parent two’ denigrates the place of both fathers and mothers.
“Fathers and mothers are not interchangeable but have quite distinct roles to play in the care and nurture of their children.”
An Identity and Passport Service (IPS) spokeswoman said: “It is essential that any parent provides the necessary information on their status as parents or guardians when applying for a passport on behalf of their child.
“This protects the interests of the child and ensures that IPS are able to issue passports securely and safely to the right person.
“The passport application form is therefore being updated to incorporate same-sex parents.”
A similar change was implemented in America earlier this year.