Dowden said the UK "can no longer guarantee the safety" of the deal with Huawei and said that US sanctions represented "a significant material change" which meant the UK had to change course.
Boris Johnson's government had earlier this year ignored US warnings against agreeing to hand Huawei a "limited" role in setting up its 5G network.
However, Johnson's official spokesman said on Tuesday that sanctions imposed on Huawei this year by the Trump administration were a "game-changer" which meant that the UK has no choice but to change course.
"By the time of the next election, we will have implemented an irreversible path to the complete removal of Huawei equipment from our 5G networks," the spokesman said.
Despite the phased removal of Huawei from the UK's 5G network, the government has no plans to remove the company from 2G, 3G, 4G, or its broadband network.
The decision will delay the roll-out of 5G by at least two years, a spokesperson for Johnson indicated, while adding substantially to the overall cost.
Oliver Dowden, the UK Secretary of State for Digital, Culture, Media and Sport, announced the decision to the House of Commons on Tuesday afternoon after Prime Minister Johnson chaired meetings with his Cabinet the UK's National Security Council in the morning.
Johnson has in recent weeks been under growing pressure to undo his decision earlier this year to grant Huawei a limited but significant role in developing the UK's 5G.
The prime minister riled Members of Parliament in his own Conservative party when he struck a deal with Huawei.
In March, he suffered a rebellion from Conservative MPs and the first real challenge to his power since winning the UK's general election in December when almost 40 voted against his government in Parliament.
Opposition to the deal with Huawei has grown since then, amid fury over China's handling of the COVID-19 pandemic and its recent decision to defy the UK and others and impose national security laws on Hong Kong.
The government's announcement on Tuesday could yet face further resistance from Conservative MPs, however.
Those leading calls for the Huawei deal to be scrapped have this month warned that the firm should be totally removed from UK networks in 2023, before the UK goes to the polls for its next general election.
Around 60 Conservative MPs are reportedly threatening to complicate Johnson's legislative agenda by attaching amendments to multiple pieces of legislation until he agrees to accelerate the removal of Huawei.
The UK deal with Huawei also angered allies in the White House, with President Trump hanging up on Johnson in an "apoplectic" phone call. The US warned that the deal with Huawei would give China a back door into western intelligence sharing.
Recent sanctions on Huawei by the Trump administration played a big part in the UK decision to phase out the firm.
The US sanctions are designed to stop Huawei using US-produced equipment to make semiconductors, creating concern in London that the firm would use different technology with an additional security risk.
Sir John Sawers, former head of MI6, last week boosted Conservative MPs calling for the deal to be binned when he wrote that US sanctions meant Johnson's government would have to exclude the telecoms firm from UK networks.