Mr Hamilton told BBC Radio Ulster's The Sunday News that it will support up to 25,000 additional assessments and 12,000 extra treatments.
This will be across a wide range of specialities including orthopaedics, gastronenterology and neurology.
Mr Hamilton said around 80,000 patients would benefit from the £30m investment.
Last month, it emerged that the number of people waiting for a first outpatient appointment in Northern Ireland has increased by nearly 37% in a year.
In December 2015, there were 236,365 people on waiting lists, compared to 171,866 the year before.
The number of people waiting more than 18 weeks for a first outpatient appointment has more than doubled.
Mr Hamilton said the funding of £30m is coming out of the extra £128m allocated to his department's 2016/17 budget.
He said that in November, £40m had been invested to tackle the issue of waiting lists.
Mr Hamilton said he "appreciated the frustration many people had" with regard to waiting lists and that he expected the figures to "go down over the months ahead".
"This is an additional £30m, over and above the additional £40m we put into waiting lists back in November, now starting to work its way through the system," he added.
"Really, from the start of this year, from January, we will have been employing £70m more on top of what we already spend through the system tackling waiting lists.
"This will keep the momentum going that we have already started in tackling our unacceptably long waiting lists."
Health Minister Simon Hamilton has pledged £30m in funding for the health service in Northern Ireland to tackle the issue of waiting lists.