The meme-inspired cryptocurrency reached above $0.16 on Tuesday morning, which saw it return into the list of the top 10 most valuable cryptocurrencies.
Mr Musk, who is a vocal crypto advocate and dogecoin investor, has said he will make cracking down on cryptocurrency scam accounts on Twitter a priority as its new owner.
Other potential changes to the social media platform could include methods to tip other users in cryptocurrency, or using crypto micropayments to verify that a user is a real person and not a spam bot.
The overall cryptocurrency market rose more modestly by around 5 per cent following the news of Mr Musk’s Twitter takeover, bucking a downward trend that had seen its market cap slide from above $2.1 trillion to below $1.8 trillion since the start of April.
Dogecoin’s sudden price increase follows a trend in recent years for the “joke” cryptocurrency to react to comments or actions made by Mr Musk.
Dogecoin founder Billy Markus responded to the price rise by tweeting: “If only Elon bought Twitter every day.”
In February 2021, Mr Musk offered to buy out so-called dogecoin whales in order to transform it into the “currency of the internet”, having previously bought some of the cryptocurrency for his infant son “so he can be a toddler hodler”.
He tweeted at the time: “If major dogecoin holders sell most of their coins, it will get my full support. Too much concentration is the only realy issue imo. I will literally pay actual $ if they just void their accounts.”
Dogecoin’s all-time price high last May coincided with Mr Musk’s appearance as the host of Saturday Night Live, during which he made frequent references to the cryptocurrency.
The price peaked close to $0.70, however subsequently crashed to around $0.10 before its staging its latest recovery. Despite the volatility, dogecoin is still up more than 7,000 per cent over the last two years.