Final answer:
John Tyler was the first vice president to become president after the death of President William Henry Harrison in 1841.
Step-by-step explanation:
The first vice president to assume the office of president following the death of a sitting president was John Tyler. He became the 10th President of the United States after the death of President William Henry Harrison in 1841. Harrison had succumbed to pneumonia only a month after taking office, which led to Tyler's unexpected ascension to the presidency. This set an important precedent for vice presidential succession.
In contrast, the only vice president to become president due to a resignation was Gerald Ford, who succeeded President Richard Nixon after his resignation in 1974.