Vasava's name was proposed by acting Speaker Mangubhai Patel and supported by Chief Minister Anandiben Patel and Leader of Opposition Shankarsinh Vaghela.
Mangubhai declared, after a voice vote, that Vasava had been elected unopposed as the Congress also supported him.
After today's election, Chief Minister Patel and Vaghela led to him Speaker's chair.
Vasava (43), who belongs to a tribal community, was earlier a cabinet minister in charge of forest and environment, tribal development and parliamentary affairs.
This will be his second term as the Speaker. He had been elected as the Speaker in February 2011 after the death of Ashok Bhatt.
The Speaker's post became vacant after Vala was appointed as the Karnataka Governor by the NDA government.
Vasava said on this occasion that the responsibility of running the House smoothly falls not only on the Speaker but every member of the House, and he expected cooperation from the members.