Appleton was confirmed as Ian Holloway's successor at Blackpool on Wednesday evening, ending a 12-month spell at Fratton Park in which the 36-year-old won numerous plaudits despite Pompey suffering relegation from the Championship while in administration.
Ashley Westwood has followed Appleton to the north west to act as first-team coach at Bloomfield Road and Portsmouth put a statement on their official website wishing both men well.
It read: "Portsmouth Football Club can confirm that we reluctantly gave Michael Appleton permission to speak to Blackpool and that he has since agreed to become their new manager.
"Michael has done an incredible job in very difficult circumstances at Pompey and we have done what we can to keep him at Fratton Park. However, he is an ambitious manager with a growing reputation and has deservedly attracted interest from other clubs.
"First team coach Ashley Westwood has also left Pompey to link up with Appleton at Blackpool. We thank them both for the work they have done here and wish them well for the future."