The bakery chain is moving into 27 Pride Hill, which was previously occupied by supermarket retailer Waitrose.
It means the branch further down Pride Hill will be closing.
"We will be relocating our existing shop at Pride Hill in Shrewsbury to a new unit later in the year and we will share more information when it becomes available," Greggs said in a statement.
Halls Commercial worked on behalf of a private client to secure the new tenant for the large premises.
James Evans, head of commercial at Halls, said: “The letting of 27 Pride Hill has filled a huge hole on the main retail high street of Shrewsbury.
"It’s no secret that it’s been a challenging market for retail over the last few months, however, this is a real positive for the high street.
"Greggs is a national chain and will be expanding its presence in the town to a larger premises creating a number of new jobs.”