Javid unveiled the coin on Saturday which is inscribed with the words "peace, prosperity and friendship with all nations" and the date of January 31, metro.co.uk said in a report.
Around three million Brexit coins will start circulating in the UK from Friday (Brexit Day), with another seven million to be minted later in the year.
Javid had previously ordered a batch of coins marking the original Brexit date of October 31, but an extension to the departure deadline was agreed at the last minute.
About a million of them had to be melted down, with the metal kept aside until a new date was confirmed.
The text on the new coin has remained the same despite the change of dates.
Javid, who is also Master of the Mint, will present a coin from the very first batch to Prime Minister Boris Johnson this week.
The Royal Mint will also open its doors for 24 hours to let people strike their own Brexit coins, the metro.co.uk said in the report.
Coins can only normally be struck as part of an organised tour. The coin producer regularly issues commemorative currency, with a notable set minted to represent each of the sports played at the 2012 London Olympics.
The idea for a Brexit commemorative coin was first pitched by former Chancellor Philip Hammond, although he reportedly planned a batch of just 10,000 pieces.
Meanwhile, the European Parliament is expected to rubber-stamp the withdrawal agreement on Wednesday after it was signed by Johnson and the EU's representatives.
( With inputs from IANS )