Fusilier Sam Brownridge, 23, died on Sunday while serving with the Mortar Platoon of the First Battalion, The Royal Regiment of Fusiliers.
The Ministry of Defence announced the news in a statement on Tuesday but has not yet confirmed the cause of death, describing it only as a "non-battle injury".
Described as "fun loving and fiercely loyal," Fusilier Brownridge grew up in Cannock, had a daughter called Marcè and had been a part of the platoon for almost two years.
Fellow mortarman Fusilier Ben Cribb paid tribute, saying: “Sam was the mate who was always there when I needed him and always had the right answer for any problems I had.
"He loved to talk about cars, Land Rovers and a home he hoped to buy in Wolverhampton.
"I’d spent almost every day with him on the tour. He was a good soldier, a mortarman who always strived to do his best at his profession.”
The Fusiliers are in Estonia for Operation Cabrit, the codename for the British Army's deployment to Eastern Europe as part of NATO's deterrent against Russia.
Around 900 British soldiers, the bulk of which are Fusiliers, are working alongside Danish, French, and Estonian troops to strengthen defence in the Baltics for NATO's "Enhanced Forward Presence".
Captain Dave Davies, Officer Commanding Mortar Platoon, said: “Fusilier Sam Brownridge was the epitome of what it means to be a mortarman. He was a solid pair of hands that took pride in learning and getting to grips with a highly specialised and unique skillset.
"He was a truly well-liked Fusilier, who brought laughs wherever he went. As a father, he often spoke of his daughter, Marcè, and she was the centre around which he conducted himself daily.
"He endeavoured to be the best father that he could. I believe that he had truly found his home within Mortar Platoon and leaves behind positive memories with all who he served with.”
Fusilier Brownridge joined the Army in January 2017 and completed his initial training at the Infantry Training Centre in Catterick before being posted to the First Battalion.
He moved from Z Company to the Battalion’s Mortar Platoon in January 2019 and had been to Canada on exercise before completing the Bulldog Armoured Fighting Vehicle Driver’s Course in preparation for deployment to Estonia.
In a statement, the Army described him as "a petrol head to his core" and said he had worked hard on his fitness in preparation for competing for the Army Enduro Motorcycle Racing Team.
"He will be remembered as good humoured, generous, warm, devoted to his friends and family," the statement added.
Lieutenant Colonel Christopher Head, Commanding Officer, First Fusiliers Battlegroup, said: “Fusilier Brownridge was everything we want in a young infantry soldier. Fun loving and fiercely loyal to his mates, hardworking, determined and professional in everything he did, and always up for a new challenge, he was a Fusilier through and through.
"Throughout the infantry, mortarmen are well known as unfailingly tough soldiers, who work hard and play hard, relishing the tight knit community the Mortar Platoon offers.
"Fusilier Brownridge was the epitome of a mortarman and wore his qualification badge with great pride.
"I am proud to have served with Fusilier Brownridge. He will be missed terribly, and this tragedy has shaken the First Fusiliers family to its core. At this most difficult time, my heartfelt condolences, thoughts and prayers are with Fusilier Brownridge, his family, friends and fellow soldiers. Once a Fusilier always a Fusilier.”