The branch of the fast-food chain will be Shrewsbury's third, and will be built on the site of the former Dragon King Chinese restaurant on Old Potts Way.
The Chinese restaurant building, next to Cineworld, will be demolished to make way for the new 4,000 sq ft restaurant.
The McDonald's will be the third in Shrewsbury to operate both a drive-through and 24-hour opening, along with restaurants at Meole Brace and Battlefield.
It will employ up to 60 people in what was Fatty Arbuckles, prior to being the Dragon King.
The proposals include the reconfiguration of the existing car park to facilitate the larger unit and drive-thru lane with an overall loss of 44 parking spaces to 414, including 18 reserved for blue badge holders.
A decision to approve the plans, from ESN (Scotland) Ltd, was taken by Shropshire Council's Northern Planning committee on Tuesday afternoon.
Concerns were raised by some members of the committee over the 24 hour opening and plans to fell 29 trees, but the application was approved by six votes to one, with one abstention.
Planning committee member Councillor Ted Clarke had read out submissions from two councillors opposed to the plans – Councillors Tony Parsons and Rosemary Dartnall, who both represent Bayston Hill, Column and Sutton.
Councillor Parson's submission said: "I strongly disagree that conditions on the opening ours are not necessary. This site is very different to the Meole Brace site."
He added: "I would suggest there is a need to restrict the opening hours on this site between 7pm to midnight with the premises to close throughout the night."
Councillor Dartnall said: "Allowing 24 hour trading will change the nature of the retail park."
Councillor Steve Davenport, a committee member, did speak in support of a restriction on the opening hours, saying: "We have got to put a closing time on it. You will just get a flood of everyone else around wanting to mirror the opening times. We have to do everyone a favour, including the other businesses and put a time limit on it."
Council planning officer Jane Raymond told the committee that any issues relating to the 24-hour opening would be picked up by the council's licensing officers – who could then take action.
The committee was also told that the 29 trees being felled would be replaced by 17 higher quality trees.
The application was approved with no restriction on opening hours.