Four Royal Air Force Tornado GR4s joined the co-ordinated missile strikes at 2am on Saturday, launching Storm Shadow missiles at a base 15 miles west of Homs.
Mr Johnson said Mrs May will be making a statement in the House of Commons on Monday and it will give parliamentarians a chance to hold the executive to account.
The strikes, in collaboration with the United States and France, are in response to an alleged chemical attack on the Syrian town of Douma last week.
She declined to say whether Bashar al-Assad should stay in power and said talks with allies would continue on finding a political solution to the civil war.
"There is a wider question on the future political solution for Syria and that is a matter that we will continue to pursue in diplomatic and political channels with our global partners and allies", May said. "It is not about regime change", May said in a statement.
Britain has blamed Russian Federation for the poisoning - a charge vehemently denied by Moscow which has accused London of failing to come up with evidence for its claims.
The Syrian regime has a history of using chemical weapons against its own people in the most cruel and abhorrent way.
May said while the strike was targeted at Syria, it sent a message to anyone who used chemical weapons.
"This is the first time as Prime Minister that I have had to take the decision to commit our armed forces in combat - and it is not a decision I have taken lightly".
Britain's defense ministry said "very careful scientific analysis" had been applied to maximize the destruction of stockpiled chemicals while minimizing any risk of contamination to surrounding areas.
"I have done so because I judge this action to be in Britain's national interest".
Williamson told BBC radio that all British crews returned safely and early indications were that the strikes had been "highly successful".
She said that at an emergency cabinet meeting in London on Thursday "we agreed that it was both right and legal to take military action" after hearing legal advice.
May is not obliged to win parliament's approval before ordering military action, but a non-binding constitutional convention to do so has been established since a 2003 vote on joining the USA -led invasion of Iraq.
British lawmakers voted down taking military action against Damascus in 2013, in what was widely viewed as an assertion of parliamentary sovereignty on the use of force. "The opposition does not operate helicopters or use barrel bombs".
But she was accused of "riding the coat-tails of an erratic USA president" by the Liberal Democrats, and "taking instructions" from Washington by Labour.