Education secretary Gavin Williamson unveiled the plan during his speech to the Conservative Party Conference last month.
He also pledged to open 16 to 19 maths schools in every region of the country.
Mr Williamson said that Apprenticeships, technical and vocational education are “just as valuable as university education”.
Institutes of Technology are collaborations between further education providers, universities and employers. They specialise in delivering higher technical education (at Levels 4 and 5) with a focus on STEM subjects.
In April, the government announced funding of £170 million for 12 Institutes of Technology, with the first ones opening their doors this term.
Mr Williamson said the additional £120 million will bring the number of institutes up to 20 in total.
The institutes are aimed at young people taking T levels or A levels who want to progress to higher technical education as well as adult learners wanting to learn new skills.
Maths schools, meanwhile, are 16 to 19 institutions that offer A levels in maths as well as similar subjects like computing and the sciences. Currently only two are open – in London and Exeter – but Mr Williamson unveiled plans for a third in Durham during his speech and said 11 would be opened in total.
Speaking about the Institutes of Technology, Mr Williamson added: “They have the potential to transform high-level technical education. Bringing together further education colleges, universities and employers but we don’t have enough of them to serve the whole country. We will make sure every young person in every part of our country gets the chance to gain the high level technical skills that they, and we, need.”
The Confederation of British Industry (CBI) has welcomed the plans. Its chief UK policy director Matthew Fell said: "Expanding high-quality technical education and training is a top priority for employers who will welcome this extra investment. By bringing firms, colleges and higher education together, these Institutes of Technology can open the door to great careers or further training.”
On the maths school plans, he added: “More than four in five businesses rank developing STEM skills among their top three priorities for action, so a specialist maths schools in every region will help to plug this gap.”