The standard procedure for cleaning a varnish brush is to rinse in mineral spirits and then wash with soap and water. The problem is the large number of times you have to wash to achieve a good lather, which indicates the bristles are clean.
You can speed the cleaning by rinsing the brush in lacquer thinner after two or three rinses in mineral spirits. The lacquer thinner removes the oiliness of the mineral spirits so the lather can be achieved after only one or two washings.
You can substitute acetone or brush cleaner for the lacquer thinner. In fact, you can do all the rinsings in lacquer thinner, acetone or brush cleaner, but these are more expensive than mineral spirits.