The Bears worked out Johnson a few weeks ago, but did not sign him to a contract.
Johnson, 26, is a former sixth-round pick of the Saints back in 2013. He spent just over a year in New Orleans before he was waived at the start of the season.
The Patriots later signed him to future/reserve contracts in each of the next two seasons before releasing him coming out of the preseason.
In 2015, Johnson appeared in one game for New England and recorded just one tackle.