This question concerns relatively recent events, so I am not sure if it fits the 20 years rule of the subreddit, but I will try to give it a go anyways. To understand Than Shwe’s succession, we first need a bit of context.

Than Shwe rose to power in Myanmar in 1992, following what can be considered a palace coup against the previous military leader, Saw Maung. His reign was brutal, like his predecessors, and of course corrupt, as under his rule the military leaders turned into business tycoons and enriched themselves even further.

During his rule, the military regime felt increasingly illegitimate, particularly since it didn’t respect the 1990 election results, and sought to reinvent itself. In 2003, the military announced that it would follow a seven-step “roadmap to democracy”. This was clearly not an attempt to transition to democracy but rather an institutionalisation of the role of the military.

One of the steps of the roadmap to democracy was the drafting of a new constitution. In 2008, the junta organised a referendum on this constitition, which was considered as rigged by all foreign observers. It passed with 93% approval. According to this new constitution, 25% of seats in parliament are to be reserved to the military, and their votes are always needed for major decisions.

This way, Than Shwe created the illusion that a democratic transition was taking place while in reality power remained in the hands of the military. As he was getting older and his health was deteriorating, he looked for a potential successor.

Thein Sein had been rising through the ranks of the military for a while. He had been the chair of the National convention, which drafted the 2008 constitution. He also became acting prime minister in 2007, and was seen as the public face of the junta, which he represented at ASEAN and UN meetings.

Than Shwe considered him to be an “acceptable face” for the regime during the transition. He was not seen as a threat to Than Shwe’s power, who sought to keep influencing political decisions behind the scenes. Thein Sein was made chairman of the USDP (United Solidarity and Development Party), the party that represents the interests of the junta.

One of the following steps of the roadmap to democracy was the organisation of new elections, which took place in 2010. These elections were boycotted by Aung San Suu Kyi’s party, the NLD, since they were seen as unfair, particularly due to the 2008 constitution which guarantees that the military keeps 25% of the seats. The USDP won this rigged election and Thein Sein became president of Myanmar in 2011.

Sources :

The Myanmar's Road Map to the consolidation of military authoritarianism, Paulo Sérgio Pinheiro

Burma’s Rigged Road Map to Democracy, Htet Aung for the Irrawaddy newspaper

Burma, What everyone needs to know, David I. Steinberg