The sale price includes the company's debt, which stood at £106m at the end of 2011, the last year for which accounts are available.
Lloyds Banking Group, which is 40% owned by the taxpayer, provided a debt- funding package to support the transaction.
WIG returned to a pre-tax profit in 2011 with earnings of £2.6m, after posting a loss in 2010, and claims a current turnover of around £20m a year.
The company was previously backed by private equity funds, including Royal Bank of Scotland Equity Finance and Penta Capital.
WIG acquires, manages and operates wireless cell sites on rooftops and masts for mobile phone operators.
The business was established 15 years ago, employs over 50 people in the UK and operates more than 2000 active sites.
Chief executive Scott Coates, who joined the business from RBS after its original investment in the company in 2006, said: "Wood Creek is an investor with the skills and experience required to help us take WIG to the next level. It is an exciting time for our industry with 4G deployments taking off and significant investments in spectrum and network needed across the board."
WIG, which has previously bought telecoms towers from the likes of Scottish Hydroelectric owner SSE and Scottish Water, plans to expand further in the UK and Europe.
Lloyds director Simon Sweeney said: "WIG is a long-standing customer of Lloyds, who we have supported through their growth strategy and acquisition plans.
"We are really pleased to help fund this deal and continue to support a high- calibre management team alongside new owner Wood Creek, who bring significant industry experience and capital to support the next stage of development for the business."
Matt Sandoval, managing director at Wood Creek, said: "Wood Creek is delighted to be adding WIG to its portfolio of communication infrastructure investments, which includes towers, spectrum and technology patents related to broadband and mobile communications."