In the speech, which was streamed live on his Facebook page from Minneapolis, the 66-year-old Franken said he doesn't plan to "give up my voice."
"I may be leaving the Senate but I'm not giving up my voice," Franken said. "We still have a lot of work to do together on issues ranging from net neutrality to climate change."
Franken also got emotional while talking about his wife, Franni Bryson. The two have been married since 1975.
"Whatever it is that we do next we will do it together," the former Saturday Night Live writer said. "While I can never thank her enough for her love and support, I am willing to spend the rest of my life trying, honey."
Franken formally announced his resignation from the Senate on Dec. 7 after a majority of Senate Democrats called on him to resign. Franken will remain in office until Jan. 2, and will be replaced by Minnesota Lieutenant Governor Tina Smith until a special election in November 2018.
In his speech Thursday, Franken called Smith "my friend," adding that she is "worthy of the incredible support that I've received."
"We still have a lot of work to do together on issues ranging from net neutrality to climate change," Franken told the crowd of supporters. "We still have to be ready to speak out for economic justice and to defend the truth."