Four are going to Oxford and three are going to Cambridge to study subjects including history, biochemistry and engineering.
The group celebrated their achievement by dining with college principal Martin Ward.
Shrewsbury Sixth Form College has a programme for those who wish to study at high-ranking universities and Mr Ward said he could not be more pleased. He said: "We are delighted that the hard work and ability of these exceptional students has been rewarded with much-coveted conditional offers of places at colleges at Oxford and Cambridge.
"They have taken advantage of all the support on offer and deserve every success".
The prospective Oxford students are David Parton, who will read Law at Jesus College, Isobel Goodman, who will read History/French at Worcester College, and Jasper Syms, who will read Engineering Sciences at Magdalen College, Oxford.
Morgan Rogers will read Maths with Physics at Magdalene College, Cambridge, while the university has also offered places to Fergus Walters to read Natural Sciences at St Catherine's College, Harriet Jackson to read Geography at Downing College, and Hannah Webb, who will read Biochemistry at St Catherine's College.
Steve McAlinden, assistant principal at Shrewsbury Sixth Form College, said: "We are passionate about providing every student with the appropriate support to help them achieve their ambitions after leaving SSFC."
The seven students will sit their exams in a few months and will receive the all-important results in summer.