The 20-year-old left-arm seamer got his visa on Tuesday afternoon. His flight is due to leave at 10:15 a.m. local time on Wednesday.
The Bangladesh national team will begin its preliminary camp for the England series the same morning, but their pace ace will be off to that country at that time, reported bdnews24.com.
Mustafizur will feature in the Natwest T20 Blast and Royal London One-Day Cup. Each of the tournaments are being played among 18 teams who are divided into two groups of nine.
Sussex will play against Essex in the T20 Blast at Chelmsford on Thursday.
Taking this game into account, Mustafizur will be with the team for seven matches -- considering both the tournaments -- while the number will go up if Sussex qualify for the knockouts in either competition.
On July 1, Mustafizur had told reporters, "It will be great if I can go to Sussex. England comes first (when talking about) cricket, so it will definitely feel good to be there. If I am given the opportunity I will try to give my best."
Sussex announced the news of signing Mustafizur on March 2 earlier this year. He was supposed to go to England at the beginning of June.
But the youngster returned from the Indian Premier League (IPL) with a hamstring injury that delayed his departure.
Sussex, however, did not give up and gave Mustafizur more time but the delay stretched on.
Mustafizur then regained his fitness at the start of this month before having to wait for the visa.
Bangladesh's top all-rounder Shakib Al Hasan and opening batsman Tamim Iqbal had played in England's county cricket competitions.
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