Matthews was born in Newport, South Wales, at the then Lydia Beynon Maternity Hospital. Matthews returned as an adult to include the manor house that housed the hospital within the Celtic Manor Resort. He grew up in the town of Newbridge, Caerphilly. He studied at Swansea University and received a bachelor’s degree in electronics in 1969.

Matthews’ first enterprise was started in collaboration with fellow Briton and Microsystems employee Michael Cowpland in 1972. To raise seed money for future enterprises they had planned, the pair intended to import and sell electric lawnmowers built in the UK. Conventionally, and from accounts by Matthews, the name Mitel is thought to be a contraction of “Mike and Terry Lawnmowers”. However, Cowpland is quoted as saying that it stands for “Mike and Terry ELectronics”. This first endeavour was a fiasco; the shipping company carrying the first batch lost the container. When the lawnmowers finally arrived, the ground was covered with snow in the Canadian winter and no one would buy them. Matthews later said “That taught me a key lesson – the importance of timing. The shipping company lost the lawnmowers! By the time they showed up no-one wanted them, as you can’t cut grass when it’s covered with snow.”

Matthews bought Celtic Manor in 1980, ploughing £100m into the project. Firstly the 19th century Manor House was renovated, while in 1991 plans were unveiled to develop two new golf courses and a convention centre between the manor and the River Usk. Matthews had become friends with golf course architect, the late Robert Trent Jones Snr, whose family roots were in Aberystwyth. Work began on the ‘Roman Road’ course in 1992, named after the main route connecting the former Roman fortress of Caerleon with the town of Caerwent, which crosses the land. In 1994 the 4,000-yard ‘Coldra Woods’ golf course was started, as well as the £10m golf clubhouse hotel.

Later, the pair realized that the then-new technology of microprocessors and other semiconductor devices would make a similar change in the market for small PBXs. The SX200 PBX launched to immense success, being cheaper to purchase, quicker to install and far more functional. Mitel became one of the more successful manufacturers of small PBX systems and telecom semiconductors in the world, floating on the New York Stock Exchange in 1981.

In 1985, British Telecom bought a controlling interest in Mitel. Cowpland would later form the company that became Corel, and Matthews later founded Newbridge Networks.

In 1986, Matthews drove Newbridge to become a leader in the worldwide data networking industry, manufacturing data communications products, especially ATM devices and routers. In 2000 the company employed more than 6,500 employees with recorded FY 1999 revenue of $1.8 billion. Later in 2000, Newbridge was acquired by Alcatel for $7.1 billion. Matthews’ personal stake in Newbridge was valued at over a billion dollars, and as a result of the transaction he became the largest single shareholder in Alcatel.

On 10 June 1994, he was appointed an Officer of the Order of the British Empire (OBE) for services to the communications industry.

In 1998, he was elected as a Fellow of the Royal Academy of Engineering.

In 2000, he reacquired the Mitel PBX business and company name, taking it private. He has invested heavily ($600 million by 2006) in Mitel to turn it into a broadband communications company. The company has made significant investments in enterprise Voice over IP telephony technology. Mitel’s manufacturing business was spun off as BreconRidge. The company acquired Intertel in April 2007. Mitel went public again in 2010. Mitel announced the purchase of Aastra Technologies in November 2013. Mitel announced the purchase of Mavenir Systems in March 2015. Mitel announced the purchase of Polycom in April 2016, however, the deal fell through and Polycom instead merged with private equity firm Siris Capital Group. In July 2017, Mitel announced they had reached a deal to buy ShoreTel for $430 million, increasing the size of the company to 4,200 employees. On 24 April 2018, the company announced it would be bought by an investor group led by Searchlight Capital Partners.

On 16 June 2001, he was conferred the honour of Knight Bachelor in the Queen’s Birthday Honours for services to Industry and to Wales. He was knighted by HM The Queen at an investiture in Buckingham Palace.

Celtic Manor was Hotel of the Year in 2002, and won two European Design Awards in 2001 – one for the interior designers, Goff Associates, and one for its spa from the International Spa Association. Matthews commented that: “I think the resort can act as a magnet to draw new investment into Wales from across the UK and overseas. I did my best to put up a building that you can see from the West End of London and I didn’t come far short of it!”.

Matthews has received honorary doctorates from the University of Wales (Glamorgan and Swansea) and Carleton University. In 2006, he was awarded an Honorary Degree (Doctor of Engineering) from the University of Bath.

In 2011, he was appointed Patron of the Cancer Stem Cell Research Institute at Cardiff University.

In September 2014, Matthews was appointed chairman of the Swansea Bay City Region Board. The Swansea Bay City Region Board is backing a Swansea Tidal Lagoon project.

In January 2016, he purchased the Hilton Hotel in Newport.

On 29 December 2017, he was appointed an Officer of the Order of Canada (OC) for his exceptional achievements as a high-tech entrepreneur and investor, and for his contributions to community development through charitable endeavours. He was invested by the Governor General of Canada at Rideau Hall on 20 November 2018.

On 1 November 2019, he was awarded an honorary doctorate from the University of Ottawa.