Mohamed Abrini - the so-called "man in the hat" - came to the UK in July 2015 and was given the money in a park, Kingston Crown Court heard.
Zakaria Boufassil, 26, who is accused of handing over the cash, denies preparing for acts of terrorism.
A second man, Mohammed Ali Ahmed, has pleaded guilty to the same offence.
Abrini became known as "the man in the hat" following his suspected involvement in the Brussels terror attack in March this year, which killed 32 people at an airport and metro station, the jury heard.
Prosecuting, Max Hill QC told the court Abrini is also suspected of being connected to attacks in Paris on 13 November 2015, which killed 130 people.
Mr Hill said Abrini travelled to the UK between 9 and 16 July 2015.
He said there "can be no doubt" the money was handed over to him while in the UK "with the intention of assisting acts of terrorism".
"That much is clear from the guilty plea by Mohammed Ali Ahmed. Mr Boufassil, denies that he personally intended to assist in the preparation of terrorist acts.
"We suggest he is lying. We suggest that he was clearly acting together with Ahmed when the money was handed to Abrini," he added.
The court heard that Abrini, a Belgian citizen of Moroccan descent, arrived at Heathrow on 9 July and headed to Birmingham by coach the following day.
There was telephone contact between the men - but also technical evidence that their phones had been in close proximity.
According to analysis of mobile phone masts, during 10 July Abrini's mobile phone and those of Mr Boufassil and Ahmed were logged as being in Small Heath Park in the city.
The following day, the three phones came together again in the same location.
Mr Hill said: "You can be sure that Ahmed, Abrini and Mr Boufassil met that day - that was the handover of the money to Abrini."
The £3,000 allegedly came from a bank account set up by another man who had previously left the UK to fight with the self-styled Islamic State group (IS) in Syria.
Most of it was from benefits payments, the court heard.
"The actual use of the money handed to Abrini is not part of the offence charged," said Mr Hill.
"There is no clear evidence one way or another. If it is suggested to you that Abrini may or did use some of the cash given to him to gamble in a casino, that does not undermine the criminal offence.
"What matters is the conduct in question, the handing over of the cash to Abrini and the intention behind the handover. What they do with it is another matter."
Abrini, currently in custody, was an associate of two men believed to be responsible for the Paris attacks - Salah Abdeslam and Abdelhamid Abaaoud.
His brother had also been killed fighting in Syria for IS, the court heard.
Following the alleged handover, Abrini moved on to Manchester before flying back to Belgium from Birmingham.
He was questioned about the UK trip by Belgian investigators, the court heard.
When his phone was later seized, police found that it contained a photo of Small Heath Park.
The trial continues.
A suspect in the Paris and Brussels terror attacks was handed £3,000 during a secret meeting in Birmingham months before the killings, a jury has heard.