The Suffolk-based tree firm, which works mainly in utility arboriculture, will continue under the management and leadership of Halley McCallum, and its current directors.
The sale includes two sister companies of bts – tbf Traffic and tbf Scaffolding, also under McCallum's management. No contracts are affected by the transaction.
The companies will remain distinct and will continue to operate from its head office in Needham Market and will maintain offices in Telford, Newark and Elgin.
McCallum said: "Joining forces with RSK gives us access to a range of new and exciting markets, such as HS2 and other contracts, for which we’re keen to get on tender lists.
"RSK has long provided arboricultural consultancy services and has recently moved into the vegetation management marketplace. Collaboration with our tree and vegetation management services will lead to new opportunities for our staff and businesses as we move confidently to an exciting future."
BTS employs around 150 direct staff and 150 sub-contract staff across the UK, and will turnover £22m in 2018.