Conelan was born in Wadnaminga, South Australia and received a primary education.

[1][2][3][4] At the 1939 by-election, Conelan was elected to the Australian House of Representatives as the Labor member for Griffith.

He won by only eight votes, the closest result in the House of Representatives that has ever been allowed to stand.

[5][2][6][7] Upon his defeat, Conelan became the first Queensland MP to qualify to the parliamentary pension scheme of £2000 or £8 per week.

[9] He remained involved in Labor politics, serving as president of the party's Kurilpa branch and vice-president of its Griffith Federal Divisional Executive.