Mr Zahawi will focus on getting the vaccine out across the country once vaccines have been approved, with the temporary arrangement set to last until at least next summer.
Downing Street said in a statement: “The Queen has been pleased to approve the appointment of Nadhim Zahawi MP as a Parliamentary Under Secretary of State at the Department of Health and Social Care.
“He remains a Parliamentary Under Secretary of State at the Department for Business, Energy and Industrial Strategy.”
Mr Zahawi tweeted: "Delighted to have been asked by Boris Johnson to become the minister for Covid vaccine deployment. A big responsibility & a big operational challenge but absolutely committed to making sure we can roll out vaccines quickly-saving lives and livelihoods and helping us."
Following the government's announcement, Labour's Shadow Health Secretary Jonathan Ashworth said: “Only days ago Labour called for a Vaccines Minister to oversee the huge logistical challenge of widespread vaccination.
"We now need a mass public health campaign urging uptake of the vaccine, alongside ensuring the resources are in place for GPs and other health professionals to rapidly roll this out as soon as possible.”
Earlier this week, Mr Zawahi had been critical of the government's decision to put his Stratford-upon-Avon constituency under Tier 3 restrictions once the England lockdown ends.
He wrote: “I am extremely disappointed and sad that Warwickshire will be moving into Tier 3 next week, in particular because of the effect this will have on our hospitality, tourism and performing arts industries who have already been through so much this year.
“It seems that the high numbers of infections, especially among those over 60, and hospitalisations in the north of the county have counted against us, and that restrictions in Warwickshire have been considered alongside Coventry and Solihull.
Political Correspondent Dan Hewitt on latest after new Covid vaccine minister appointed
“I spoke with the Health Secretary after the announcement on Thursday and made clear to him the very strong feelings from constituents about restrictions in Stratford-on-Avon being affected by factors in areas further away from us than from our immediate neighbours, such as Worcestershire and Oxfordshire, both of whom will be moving into Tier 2 next week."
Several vaccine candidates have announced positive results in the past few weeks, including Pfizer-BioNTech, Oxford-Astrazeneca and Moderna - with the hope some doses could possibly be rolled out before Christmas.
Before the vaccines are rolled out nationally, they need to go before the regulatory body - the Medicines and Healthcare products Regulatory Agency (MHRA).
The MHRA confirmed on Monday it had received the necessary data to progress their review into whether the Pfizer/BioNTech vaccine meets the required standards.
It is highly likely the agency will soon receive data from the Oxford/AstraZeneca vaccine, after initial trials concluded the vaccine can prevent up to 90% of people contracting coronavirus and getting seriously ill.
The regulatory body will look through all the phase trials of the vaccine, any side effects, how common they were, who experienced them, whether they were recurrent, complications, who should not have the vaccine and how effective the vaccine is.
Gordon Duff, former chairman of the MHRA, told ITV News: “What will be judged is that the benefits far outweigh any risks to any recipient of the vaccine and even if those risks are theoretical, that has to be taken into account.”