“The people have spoken,” tweeted Mr Musk, saying that 51.8% of more than 15 million Twitter users voted for the ban to be lifted.
His account was suspended in 2021 due to the risk of incitement of violence.
Twitter’s previous management acted just days after Donald Trump’s supporters stormed the US Capitol in Washington DC on 6 January.
Hundreds of rioters entered the complex as the US Congress attempted to certify Joe Biden’s victory in the presidential election. The ensuing violence led to the deaths of four civilians and a police officer.
Several months later, he launched his own social media platform, Truth Social.
Earlier this week, the Republican announced that he would once again run for the US presidency in 2024.
Musk, the world’s richest man, took control of Twitter in October in a $44bn (£37bn) deal.
He immediately embarked on a series of radical changes within the social media giant, amid concerns that he might loosen Twitter’s regulations on hate speech and misinformation.
With just over a week before the US midterm elections on 8 November, he responded to questions about whether he would reinstate Trump’s account by tweeting: “If I had a dollar for every time someone asked me if Trump is coming back on this platform, Twitter would be minting money!”
Earlier this week, he told employees that the company’s office buildings would be temporarily closed, with immediate effect.
The announcement comes amid reports that large numbers of staff were quitting after Musk called on them to sign up for “long hours at high intensity” or leave.