Pence issued a statement calling the cut "a great victory" for taxpayers even though it is half of what he proposed and is phased in over a much longer period.
Republican legislative leaders had resisted Pence's push for a 10 percent tax cut to be fully implemented by July 2014. The House approved a budget plan in February without an income tax cut and the Senate this month had backed just a 3 percent cut.
Republican House Speaker Brian Bosma said his priorities had always been that the state's budget be strong enough to avoid big spending cuts or the need for tax increases in the future.
"We believe this blend is the right blend, it's at the right amount, it's at the right time to be sustainable for the future," Bosma said.
The Republican-dominated House and Senate are both expected to vote on the two-year budget plan on Friday, which is expected to be the final day of this year's legislative session.
The proposed budget also calls for repealing the state's inheritance tax retroactive to Jan. 1 of this year, which will reduce state revenue by about $150 million. Legislators last year had approved a 10-year phase out of that tax.
The spending plan gives 2 percent and 1 percent increases for school funding over the next two years, for about a $330 million hike.
Democrats have criticized the school funding increase as inadequate after former Gov. Mitch Daniels cut some $300 million from school spending during the recession.
The budget plan would also increase state funding for road and bridge projects by $215 million a year.
Pence said in his statement that the tax cuts put the state's taxpayers first.
"The combination of a 5 percent individual income tax cut, inheritance tax repeal and additional tax relief for businesses is the right tax relief at the right time and will give a much needed boost to working families, small businesses and family farms," Pence said.