US president Mr Trump remains in charge until mid-January, when Joe Biden will take over.
Critics warn Mr Trump’s influence on the course of the Covid-19 virus during that time, as well as on a host of other issues, could be substantial.
The event, hosted by Saudi Arabia, will see G20 leaders discuss the threat of the virus as well as the economic devastation it has wreaked.
Speaking ahead of the meeting in a video message to other G20 leaders, Mr Johnson said that in March the group had committed to do “whatever it takes to overcome the pandemic and protect lives and livelihoods”.
“As we meet this weekend, we must hold ourselves to account for that promise,” he said.
“If we harness the collective ingenuity and resources of the G20, we can chart a path out of the pandemic and build a better, greener future.”
He added: “It is only by joining forces and working together that we will defeat coronavirus and build back better from this crisis.
“Our fates are in each other’s hands.”
He called on all G20 nations to follow the UK’s lead and commit to equitable global access for any Covid-19 vaccine.
Mr Johnson will be self-isolating in Downing Street all weekend, but will attend the meeting virtually on Saturday and Sunday.