The 19-year-old won the Aviva Premiership A League title with the Tigers, while he made his senior debut in the LV= Cup.
However Markham, who came through the academy set-up at Sale before moving to Welford Road, is relishing the chance to develop his game at Gloucester.
"Gloucester is a great club in a great rugby community and it's a chance for me to explore the game more and test myself against some of the best players in the country," he told the club's official site.
"It's about developing myself as a person and as a player. Gloucester have shown in the past that they're not afraid to give young players a chance and hopefully I'll get some game time as the season goes on.
"I'm really looking forward to meeting the rest of the squad and putting in the hard work in training but especially working with guys like Alex Brown, Jim Hamilton and Will James and learning from them, developing my game and making the most of any opportunities that come my way."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.