Mr Abbas defeated two other candidates, Idris Wase and Sani Jaji.
Tajudeen Abbas has been elected the new Speaker of the 10th House of Representatives.
He polled 353 votes to emerge the winner of the Speakership election.
The other contestants, former Deputy Speaker Idris Wase and Sani Jaji, polled three votes each.
Mr Abbas is the anointed candidate of the ruling All Progressives Congress (APC). He represents Zaria Federal Constituency of Kaduna State, North-west Nigeria.
The new Speaker was first elected to the House in 2011. He succeeds Femi Gbajabiamila.
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