A letter written to a former employer requesting to be considered for rehire must be addressed to a person in charge of hiring at the company. Write the letter using standard letter format, or memo format, and make it clear in the first paragraph that you left the company and wish to return. Use a sincere tone and reassure the employer that you intend to make a long-term commitment as an employee.
A letter requesting to be rehired at a company doesn't need to be long or attempt to explain every detail behind the decision. However, the letter must provide a clear reason for leaving the employer. For instance, if you left for a new position, the letter should provide the job title and name of the new employer. Briefly explain what prompted the desire to return. Often, the new job doesn't meet expectations, and it's OK to omit the specifics about what went wrong at the new place of employment, because the goal is to get an interview with the hiring manager.
A rehire letter for a military service member is similar, but includes slightly different language. The letter reminds the employer of the initial call of duty notice, mentions the Uniformed Services Employment and Reemployment Rights Act, and also mentions proof of service documents.