Parish was incumbent having replaced Ann McIntosh in 2015. He has been campaigning for a new Seasonal Agricultural Workers Scheme via the committee in recent months.
Parish won 324 votes, with Goldsmith 107 and Wiggin 137.
New Defra secretary of state Michael Gove is being urged by some MPs to split the department into farming and environment sections to give farming more emphasis as Britain introduces a new agriculture policy post-Brexit.
Clive Betts has been re-elected as the Chair of the Communities and Local Government Committee.
Betts was elected as Chair of the CLG Committee in the 2010 and 2015 Parliaments.
He said: "I am honoured to be re-elected by the House as Chair of the Communities and Local Government Select Committee. Local government faces a number of challenges over the coming years and I hope the Committee will shine a light on these issues, provide robust scrutiny of Government policy, and propose constructive solutions.
"I look forward to the wider membership of the Committee being nominated as soon as possible so we can get on with our work; there are a wide range of significant and important issues that the Committee may wish to consider for future inquiries during this Parliament. Affordable housing and the need to increase house building remain high on the agenda and there are also ongoing questions around the future of devolution, and the funding of adult social care.
"The Grenfell Tower disaster also raises issues for potential review. I believe the Committee should not seek to duplicate matters being looked at by the public inquiry, but there are issues, for example, regarding the effectiveness of building and fire safety regulations which the Committee, once formed, may wish to consider."
Parliament summer recess is from 20 July to 5 September.