Wedde started publishing poetry in 1966. He travelled in Jordan and England in the late 1960s and early 1970s, and returned to New Zealand to live in Port Chalmers in 1972. In 1975 he moved to Wellington.
From 1983 to 1990 Wedde was the art critic for The Evening Post. He co-edited The Penguin Book of New Zealand Verse with Harvey McQueen in the mid 1980s, and The Penguin Book of Contemporary New Zealand Poetry with McQueen and Miriama Evans in 1989. He became the arts project manager at Te Papa in 1994 where he curated the opening art exhibition Parade that controversially paired McCahon's Northland Panels with a 1950s refrigerator.[3]
A collection of essays, Making Ends Meet, was published in 2005.[4]