When completed, it will have space for seven patients at a time and deliver more than 125,000 treatments during its lifetime.
The unit will be the charity's third and will be 60% bigger than the first mobile chemotherapy unit it launched.
Its original unit, designed to offer treatment away from hospital, was unveiled in 2009 and cost £300,000.
Tenovus Cancer Care chief executive Claudia McVie said: "Currently, cancer patients in Wales can travel up to 150 miles for treatment.
"Every round trip to hospital can cost nearly £70 and if someone relies on public transport, these journeys can take hours.
"Our mobile support units cut journey times to hospital, making receiving treatment less stressful and less expensive for cancer patients."
Health Secretary Vaughan Gething said it would help to reduce "anxiety that can be involved in attending large, busy hospitals".
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