The announcement was made by President Trump during Prime Minister Malcolm Turnbull's visit to the United States.
Speaking at a press conference over the weekend, President Trump said the ship was a symbol of the bond shared by the US and Australia.
"As she sails the opens seas, the new USS Canberra will be a symbol to all who cross her path of the enduring friendship between the United States and Australia," President Trump said.
"There is no closer friendship."
Prime Minister Turnbull welcomed the announcement, touching on the significance of West Australian company Austal.
"Austal, Australia's premier shipbuilder, employs over 4,000 Americans and its investment is growing all the time," the Prime Minister said.
"It was an honour ... and a symbol of our alliance when the President announced that the United States Navy would name a future littoral combat ship, to [be] built at the Austal shipyard in Mobile, Alabama, the USS Canberra."
Minister for Defence Marise Payne has been asked to be the ship's sponsor.
The vessel, which will replace its former namesake decommissioned in the 1970s, is the only US navy vessel to be named for a city outside of the US. The former USS Canberra was named after Australian vessel, HMAS Canberra.
A friendship built on shared values and forged in battle. The naming of #USSCanberra is another step together as we mark 100 years of mateship between Australia and the USA. A very special honour to be asked to be the ship's sponsor. 🇦🇺🇺🇸 pic.twitter.com/PPCgwlMYKV— Marise Payne (@MarisePayne) February 24, 2018