An extra 250 temporary accommodation places and an additional 180 supported places are among the proposals contained in the strategy.
Speaking at the launch on Tuesday, Mr Dodds said the barriers homeless people faced in accessing services the rest of society took for granted had to be taken down.
"Everyone must have access to a decent home within a stable and caring community," he said.
Another key element of the proposals is a commitment to reduce the Housing Executive's dependency on bed and breakfast accommodation by 50%.
The DUP minister stressed the problems of homelessness stretched beyond that of housing, and referred to the social, educational, health and employment implications faced by those living on the streets.
"The Housing Executive's new strategy will create a modern and effective service which can make a real difference to the lives of homeless people," he said.
"Complex problems require co-ordinated solutions and the strategy recognises the need to build on the excellent partnerships between the public, voluntary and community services in the delivery of services to homeless people."
'Barrier'
Chairman of the Housing Executive Sid McDowell said the strategy provided a comprehensive framework for supporting people to escape homelessness and helping people avoid homelessness.
"More than 14,000 households came to us homeless last year," he said.
"It disturbs me that some people seem to believe there is an acceptable level of homelessness.
"We must, above all, dare to believe that homelessness can be eradicated from our community and we must commit every ounce of our energy to making it happen."
The minister insisted the issue remained a key priority of his department and announced the setting up of a working group that would cross departmental and sector boundaries.
"Its task is to break down the barriers faced by the homeless in obtaining those services that the rest of the community take for granted," he said.