Laws was a Liberal Democrat MP from 2001-2015, and was schools minister and a Cabinet Office minister between 2012 and 2015.
He worked for the banks JP Morgan and Barclays de Zoete Wedd prior to entering parliament.
Laws takes on a part-time role at the 32-strong agency, which registered revenues of £3.1m in the year to March 2017. He will advise clients in a variety of fields including education, pensions and economic policy, among others.
GK Strategy CEO Emily Wallace said: "David’s appointment is an exciting moment for GK and its staff. His Cabinet-level experience and understanding of decision-making at the heart of Government will be invaluable to the engagement campaigns we support our clients to deliver."
The firm took on former Oasis Dental Care CEO Justin Ash as its first chair last month, and earlier this week announced the launch of GK Intelligent Planning, a new division supporting property developers.
It also hired Novartis senior corporate affairs manager Andrew Nye as head of health and social care last year.
Founded in 2008, GK Strategy initially worked solely in the private equity space, but has now expanded to work for clients across healthcare, higher education and professional services. It created sister digital agency onefourzero in 2015 - it now has eight staff.
Another adviser to the business is former Labour minister Phil Hope.