Courts will be put under a legal duty to ensure that both fathers and mothers are given access to children in divorce settlements.
Parents who refuse to accept the orders will be in contempt of court and risk serious penalties or even jail.
The news will give hope to campaign groups who have argued for years that the role of fathers in bringing up their children should be enshrined in law.
Under the present system family courts tend to leave children with their mothers in the vast majority of cases.
According to the Office for National Statistics, one in three children, equivalent to 3.8million, lives without their father.
Nick Clegg, the Deputy Prime Minister, and Iain Duncan Smith, the Welfare Secretary, are understood to support the plans. The Conservatives also pledged to introduce the reforms while in opposition.
Tim Loughton, the children’s minister, said: “Our vision is to establish that, under normal circumstances, a child will have relationship with both his or her parents, regardless of their relationship with each other.
“We must do everything we can to improve the system so that it gives children the best chance of growing up under the guidance of two loving parents.
“All the evidence tells us that children genuinely benefit from a relationship with both parents, with the potential to make different contributions to their child’s development.
“The culture has shifted away from the traditional view that mothers are primarily responsible for the care of children. Increasingly society recognises the valuable and distinct role of both parents.
“We are looking closely at all the options for promoting shared parenting through possible legislative and non-legislative means.”
The decision would overturn the main finding of a major family justice review, run by businessman David Norgrove, which reported in November.
Mr Norgrove dropped a plan to allow to enshrine equal access rights in law from his final 220-page report.
He said it would put too much pressure on judges to set out the exact length of time that each divorced parent should spend with their children.
He cited evidence from Australia which suggested children were more damaged when courts imposed time limits on access to parents.
However Mr Loughton said judges made the mistake of seeing shared parenting “as being about equality of time”.
He added: “As we know, we cannot carve up a child’s existence on the basis of some spurious 50:50 split in terms of time”.
Mr Loughton described the Norgrove study as “a Government-commissioned report, not a Government report”, suggesting ministers were distancing themselves from it.
The Coalition is expected to announce the plans as part of its official response to the Norgrove report by the end of this month.
The law could be changed by amending the 1989 Children’s Act to include a presumption of shared parenting. Mr Loughton unsuccessfully tried to do this when he was in Opposition five and a half years ago.
Another option is for the Government to support a backbench bill being promoted by Tory MP Charlie Elphicke, which is due to have its second reading later this month.
Mr Elphicke’s bill requires courts and councils which are enforcing contact orders for children “to operate under the presumption that the rights of a child include growing up knowing and having access to and contact with both parents involved”.
Last night Mr Elphicke, the MP for Dover, said: “Now is the time to change the law and give our kids the best chances in life. The Government is looking at whether to give children the right to know their fathers.
“Fathers should act now by writing to their local MP and Ministers about their experiences and why the law needs to be changed. Child welfare is best served by a relationship with both parents.
“Anti-dad sociologists and weak-kneed judges have undermined the welfare of our children for too long.”
Last night Nadine O’Connor, a campaign director for Fathers4Justice, said it would be a “massive step forward”.
Ms O’Connor said: “It is a massive step forward. It is saying that Dads have as many rights as Mums. I will believe it when I see it, but the reform has to apply across the family justice system.”
Other measures from the Norgrove report, such parenting agreements detailing how childcare would be cared for after a divorce and information hubs to enable parents to carry out ‘do-it-yourself’ divorces, look set to be accepted.
Last night a Government spokesman said: “The Government fully supports the Family Justice Review’s position that the vast majority of children benefit from a continuing relationship with both parents after separation.
“We are looking closely at all options to promote this. We will publish the Government’s response to the Family Justice Review shortly.”