The centre is named after Harold Wilson, the former prime minister, because he and his wife Mary made Scilly a regular holiday retreat.
Malcolm Wicks, the lifelong learning minister, opened the centre and said that education and learning always had a special place in Harold Wilson's heart.
"A Wilson government had given us comprehensive schools, polytechnics and new universities," said Mr Wicks.
"But above all it gave us the Open University, which bore the personal imprint of the Prime Minister himself."
The Open University had drawn back into learning those groups of peple who hadn't - or couldn't - take advantage of higher education - housewives; people with disabilities; and those living in isolated communities, said the minister.
"Just as the OU helped change attitudes to higher education towards the end of the last century, local learning centres are now helping change attitudes to learning and acquiring new skills in this new century."
The new centre will offer distance-learning courses and Internet access. There will also be video conferencing facilities to enable students to link up with schools and universities on the mainland, 28 miles away.
This will help Scilly island parents to keep in contact with their children who are studying on the mainland.