The meeting will be held in 10, Downing Street, reports the BBC.
Once the UK leaves the EU on January 31, the two sides will begin talks on their future economic relationship.
Johnson has insisted a deal is possible by the end of 2020 and the process will not be extended.
After its proposed exit, the UK will enter into an 11-month transition period in which it will largely follow EU rules but will not have any representation in the bloc's institutions. This period will come to an end on December 31.
Speaking to the BBC on Wednesday morning, Brexit Secretary Stephen Barclay said that the UK and EU had agreed in the political declaration to do a trade deal by the end of this year and they were "confident" they will do that.
"Of course there will be planning within Whitehall for any eventuality, but we aim to get a trade deal.
"Both sides are clear they want a trade deal, the political declaration says it can be done to that timetable, let's be positive," he added.
Von der Leyen, a former German Defence Minister, took over from Jean-Claude Juncker at the start of December.
Besides meeting Johnson, she will also set out her vision for future UK-EU relations in a speech at the London School of Economics.
In public, EU officials have said they will do all they can to reach agreement by the end of the year although, in private, many have cast doubt on whether this is possible without some difficult compromises.
( With inputs from IANS )