The news follows the approval of the new school curriculum by the House of Commons last month, by a vote of 538 to 21.
LGBT+ rights charity Stonewall has lauded the decision as "historic", saying that the regulations mark a "significant and welcome change to how pupils are taught about LGBT+ relationships and identities".
"It's life-changing legislation that will give LGBT+ pupils the tools to make informed decisions about their relationships and their futures," the charity said in a statement released online.
The charity outlined the importance of educating children in primary schools about LGBT+ families, so that "children from LGBT+ families see themselves reflected in what they learn".
"More than 30 years on from the introduction of Section 28, this announcement shows just how far we've come," the organisation added.
Several other LGBT+ organisations have also responded positively to the news.
"We at Schools Out UK are very pleased that the Lords have backed the Relationships and Sex Education bill," Professor Sue Sanders, founder of LGBT+ History Month and chair of Schools Out UK, a charity which provides education about the LGBT+ community, tells The Independent.
"I hope it means that the Department for Education will support the work effectively and energetically. It requires training of teachers and providing resources."
Pride in London tweeted that the announcement is "brilliant news for LGBT+ children", stating: "Excellent to learn that the regulations for teaching Relationships Education and Relationships and Sex Education in England's primary and secondary schools have passed safely through the House of Lords."
AKT, a charity which provides safe homes to young members of the LGBT+ community in the UK who are experiencing homelessness or living in dangerous environments, explained the significance of the backing.
"A more inclusive education benefits everybody, but for LGBT+ young people in particular, it will enable them to learn and develop in a safer environment," the charity tweeted.
In the House of Lords on Wednesday evening, Lord Agnew of Oulton, parliamentary under-secretary of state at the Department for Education, stated: "There is no reason why teaching children about the diverse society that we live in, and the different types of loving and healthy relationships, cannot be done in a way that respects everybody’s views.
"Schools should ensure that the needs of all pupils are appropriately met and that all pupils understand the importance of equality and respect, in particular respect for difference."
Lord Agnew said that the new regulation is "clear on the teaching about LGBT relationships expected in secondary schools and encouraged in primary".
The Conservative politician added there will still be "flexibility" for head teachers to "respond to the needs of their own schools".
Professor Sanders states that while the backing of the guidelines in the House of Lords is promising, more action is needed to protect young members of the LGBT+ community.
"It seems fitting to be writing this on Lesbian Visibility Day as though strides have been made, the level of suicides and attempted suicides of young LGBT people far out way those of heterosexual youngsters, and recorded homophobic hate crimes have risen," Professor Sanders says.
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