Michael Matheson, who racked up the charges on holiday, announced he was quitting the Cabinet role on Thursday morning.
Speaking after First Minister’s Questions a short time later, Mr Yousaf told reporters he has a “reshuffle to get on with”.
Mr Matheson had been due to give a statement in the Scottish Parliament on Thursday afternoon, indicating the reshuffle could be completed later in the day.
The health secretary was expected to update MSPs on the Government’s plans to potentially raise the minimum unit price of alcohol, with 65p suggested as the new rate.
Mr Matheson accumulated the charges in Morocco over Christmas 2022, later conceding it was the result of his teenage sons using the parliamentary device as a hotspot to watch football.
Opponents repeatedly called for Mr Matheson to resign when the bill first emerged in November last year, pointing to his claim to journalists that there had been no personal use of the device, before telling MSPs days later his sons had used the data.
At the time, the First Minister – himself a former health secretary – gave Mr Matheson his backing.
But following his resignation, Mr Yousaf said it is right Mr Matheson steps aside to avoid the issue becoming a “distraction”.
The Scottish Parliamentary Corporate Body is due to release the initial findings of its probe into the spending in due course.
Announcing his resignation, Mr Matheson said: “I am conscious that this process will conclude in the coming weeks.
“I have still not received the findings of their review, however it is in the best interest of myself and the Government for me to now step down to ensure this does not become a distraction to taking forward the Government’s agenda.”
He had initially agreed to claim £3,000 of the roaming charges bill as part of his expenses allowance, while his office provision paid the rest – meaning the public purse covered the bill in full.
But after increasing pressure on the issue, Mr Matheson said he would pay the full cost himself.
Mr Matheson added he had been “enormously grateful” for the support Mr Yousaf gave to him and his family over the last year.
He has held various roles in the Scottish cabinet for almost 13 years, including the justice, net zero and public health portfolios.
In response to Mr Matheson’s resignation, Mr Yousaf told him: “It is right that, having requested that the Scottish Parliament Corporate Body review your data roaming charges from last year, that you fully engage with that process as it comes to its conclusion.
“I agree that it is therefore best for you to now step down to ensure you are able to give the parliamentary process the attention it deserves without it becoming a distraction to taking forward the Government’s agenda.”
Scottish Labour health spokeswoman Dame Jackie Baillie said: “While I welcome the news that Michael Matheson has finally gone, the fact is the First Minister has big questions to answer over his lack of judgment.
“While our NHS is in crisis, Humza Yousaf has shown his weakness by putting the SNP before our NHS.
“Now more than ever we need a health minister focused on the crisis at hand.
“It’s clear that the First Minister has no plan to save our NHS and that shuffling the SNP deckchairs will make no difference – it’s time for change.”
Scottish Liberal Democrat leader Alex Cole-Hamilton said patients “deserve better than an SNP minister who has lost their trust and could no longer focus on the day job”.
He added: “From Humza Yousaf to Michael Matheson, our NHS has known only crisis, soaring vacancies and even longer waits.”