The bridges, which were revealed at a special opening ceremony on March 21, were funded by a generous donation and a successful fundraising campaign.
They now allow visitors to move easily between both sides of the garden for the first time in decades.
The Rose Garden was originally connected by rustic bridges, but these were removed more than 80 years ago.
The new bridges were installed in early March after detailed historical research and collaboration with contractors and local planning officers.
They were made by Saram Hardwood, who worked closely with National Trust heritage curators to design them in a similar style to the 1920s originals while maintaining modern construction and safety standards.
Morden Hall Park’s general manager, Abi McNeil, said: “It has been a pleasure to invite the local community to celebrate the long-awaited opening of the new bridges and return a little bit of history to the significant part of the park.
“We are thankful to everyone who contributed to the fundraising campaign and the generosity of the Wimbledon National Trust Association.”
David Warne, chairman of the Wimbledon National Trust Association, added: “As our local property, we have been supporting and fundraising for Morden Hall Park since our inception back in 1982.
“Since 1990 we have raised over £177,500 for the National Trust, of which £87,135 has been for various projects in the park.
“We are delighted to see the new bridges installed.”
The Rose Garden was created around 1921 by Gilleat Hatfield, the last owner of Morden Hall Park, who bequeathed the estate to the National Trust in 1941.
It is thought to be the only major alteration made by Mr Hatfield to the park.