- Several accounts, such as that of former US President Donald Trump, have already been reinstated by Mr Musk.
- However, the multi-billionaire said conspiracy theorist Alex Jones would not be allowed to return to Twitter.
Elon Musk says Twitter will provide a "general amnesty" to some suspended accounts from next week.
This came after he started a poll on Wednesday asking Twitter users whether accounts that had "not broken the law or engaged in egregious spam" should be let back on the social media platform.
Several accounts, such as that of former US President Donald Trump, have already been reinstated by Mr Musk.
The world's richest man bought Twitter for $44bn (£36.3bn) last month.
More than 3.1m Twitter users responded to Mr Musk's poll, with 72.4% of them voting "Yes".
"The people have spoken. Amnesty begins next week," Mr Musk, who has 118.7m followers on the platform, later tweeted.
He also used a Latin phrase which translates to "the voice of the people is the voice of God".
Mr Musk did not give details on how the amnesty process would be carried out.
On Saturday, he reinstated the account of Donald Trump, after running a poll in which users narrowly backed the move.
But the former US president may not return to the platform, as he said "I don't see any reason for it".
He has announced plans to run again for the US presidency in 2024.
His Twitter account was suspended in 2021 on grounds that it risked inciting violence, after Trump supporters had stormed the US Capitol.
Mr Musk has also reactivated the Twitter accounts of rapper Ye (formerly Kanye West) and influencer Andrew Tate.
However, the multi-billionaire said conspiracy theorist Alex Jones would not be allowed to return to Twitter.
Infowars host Jones has been forced to pay $1.44bn in damages after falsely and repeatedly claiming that the 2012 Sandy Hook school shooting in the US, in which 20 children and six adults were killed, was a hoax.
Mr Musk wrote that his own child had died, and that he "had no mercy" for anyone who "would use the deaths of children for gain, politics or fame".
Previously he said no decision about banned accounts would be made until a moderation board had been appointed.
Mr Musk completed his $44bn purchase of Twitter on 28 October after months of wrangling.
He has since laid off half of the firm's 7,500-strong workforce, and hundreds more staff are believed to have left, following an email saying that long hours and "hardcore" work would be required of those who remained.