Goal has learned that Barca will officially announce the signing of Dest on either Monday or Tuesday having already reached an agreement over a €25 million (£23m/$29m) deal with Ajax.
The 19-year-old will not travel to Camp Nou until after his transfer is finalised, but he has already said his final goodbyes to team-mates and staff members at Johan Cruyff ArenA.
Dest will become newly-appointed Barca manager Ronald Koeman's first major signing in Catalunya, but further additions are expected before the transfer deadline in La Liga on October 5.
Goal can confirm that Manchester City centre-back Eric Garcia is top of the club's list of defensive targets, and that they are also prioritising the signing of a new striker following Luis Suarez's switch to Atletico Madrid.
The Uruguayan followed Arturo Vidal, Ivan Rakitic and Nelson Semedo out of the Camp Nou exits, and Barca are also planning to offload Samuel Umtiti, Rafinha, Jean-Clair Todibo and Martin Braithwaite in the coming days.
However, the Spanish giants will only be able to invest 25 per cent of the money raised through player sales in new signings, having exceeded the staff cost limit authorised by La Liga to manage the economic impact of the Covid-19 crisis.
Inter forward Lautaro Martinez has long been linked with a move to Barca, and although the club still see the Argentine as an option, they may have to give up on their pursuit of a man reportedly being valued at around €80 million (£72m/$93m) due to their current financial situation.
Lyon winger Memphis Depay is also reported to be on Koeman's radar, and the player admitted to being aware of Barca's interest following his exploits on the international stage with the Netherlands earlier this month.
Pressed on the possibility of bringing in Lautaro or Depay before watching his side beat Villarreal 4-0 at Camp Nou on Sunday, Koeman told reporters: “Nothing is ruled out. We are always looking for players to improve our game.
“It may be that the players you want aren't possible because of the financial situation of the club, but I've accepted this – I knew it before I arrived.”
Barca are due back in La Liga action away at Celta Vigo on Thursday, before their focus shifts to an even tougher trip to Ramon Sanchez-Pizjuan Stadium to face last season's Europa League winners Sevilla three days later.