Calling Obama a "good friend" of Ireland he stated that progress would be made on immigration reform and visas for undocumented Irish in the USA.
Gilmore also said a stronger economic climate lead by the U.S. would help Ireland.
"We are dependent on the American economy growing, so we have an interest in measures being taken that will expand the American economy and create jobs and improve trade," he said.
Fears about US multinationals being forced to repatriate profits were overblown, he said .
"Although that was mentioned in his first term, it didn't materialise at all. I think that is because there is a recognition in the US administration that investment is a two-way street," Gilmore said on RTE's Morning Ireland.
Meanwhile, President Michael D Higgins has congratulated President Obama on his re-election.
"The international community faces many daunting challenges and we look forward to your continued leadership and constructive engagement in the period ahead," wrote Mr Higgins, a human rights campaigner.
"The very close and warm relationship between Ireland and the United States has, with your help and encouragement, prospered during your tenure.
"I am confident that, under your leadership, our bilateral relations will be further advanced during the next four years.
"My wife Sabina and I send our warmest personal wishes to you and your family as you begin your second term."