A working group has spent the past two years and pound;12,000 investigating the viability of the proposal. Affiliation would cost the union about pound;300,000 a year, increasing annual subscriptions by around pound;2.
Speakers for the resolution said the TUC had shed its militant reputation of the 1970s and was well-connected in Britain and Europe, and able to provide information and training to members.
The TUC draws up common policies on workplace law, helps unions to develop new services and avoid clashes of interest, and builds worldwide links with similar bodies.
Opponents feared an exodus of members, however. Nottingham delegate Ralph Surman said: "This union is different because it has no headteachers and is not affiliated to the TUC. We stand on our own two feet and we are moderate. If we sign up to this you might as well join the NUT because they are the biggest."
Eddie Ferguson, from Belfast, said membership of the TUC "would ensure that we are no longer standing on the sidelines". The working group has voted by seven to two in favour of seeking affiliation, while the ATL executive had returned a yes vote of 40 to 17. The working group found disadvantages balanced advantages, but said the ATL was seen as a relatively high-status group whose influence might be increased by affiliation.
The two largest teaching unions - the NUT and Nasuwt - are already affiliated, as is the Educational Institute of Scotland. ATL affiliation would probably rule out any merger with the moderate Professional Association of Teachers.
Peter Smith, ATL general secretary, said: "It is entirely sensible that the entire membership should now be balloted on this issue, which has been a topic of some debate for the past two years."
Earlier the assembly had defeated an amendment calling for affiliation to be sought only if there was a 50 per cent turnout with two-thirds of votes cast in favour.