Mr Martin, who was second pick on the Jacqui Lambie Network ticket at the 2016 election, made the announcement on Friday morning.
Legal experts have raised questions over whether his local government status is regarded as an office of profit under the Crown, which would disqualify him under the constitution.
But Mr Martin said he'd gotten advice from the Clerk of the Senate in 2016 that he was eligible to stand.
"I'm saying I'm sound and if the government or senate wish to refer me to the High Court, I'll be comfortable if they do that," he told ABC Radio.
Ms Lambie resigned from the Senate this week after UK authorities confirmed she was a British citizen by descent.
She told parliament on Tuesday she hoped to one day return to federal politics.
Mr Martin emphatically denied he would stand aside to enable Ms Lambie's return, if she were to be cleared by the High Court.
"Jacqui has said publicly she's not going to ask me to resign and she has not done so," Mr Martin said.
"She's told me the position is mine."
In a separate case, the High Court this week ruled Liberal candidate Hollie Hughes was ineligible to take the Senate seat of former cabinet minister Fiona Nash.
Ms Hughes was appointed a part-time member of the Administrative Appeals Tribunal on July 1 this year.
