The trio, whose deals are subject to medicals, will be welcome additions at Bloomfield Road as new manager Jose Riga attempts to assemble a full squad ahead of the start of the Sky Bet Championship campaign at Nottingham Forest in 12 days.
Midfielder Mellis, 23, has been training with the Seasiders for a couple of weeks and has agreed a one-year deal with the option for a further year.
He made 33 appearances for Barnsley last season after coming through the youth ranks at Chelsea and he has represented England at various youth levels.
"I'm happy to be here. I've been here for two weeks now and I've got used to the place," Mellis told Blackpool’s official website. "I'm looking to come here and be successful."
Polish midfielder Cywka, who also departed Barnsley at the end of last season following their relegation to League One, has also signed a one-year contract with the option of a further year.
The former Wigan, Oldham, Derby and Reading player told the club's website: “I’ve played loads of seasons in the Championship and it’s another part of my career here, so I’m looking forward to it, it should be positive.
“I’m an offensive player looking to get a goal or to set up a team mate. If I get the chance I’ll definitely try to score some goals for Blackpool."
Defender Clarke, 32, is returning to Blackpool on a one-year contract, also with the option of a further year.
He previously spent two seasons with the Seasiders from 2004-6 before moving on to Southend and then Huddersfield, where he has spent the last five seasons.
Clarke told the club's website: "It's nice to be back. The place has changed a little bit but some of the same faces are still here, which is nice.
"I return a more experienced player and someone who can hopefully help the younger players, maybe be a bit of a role model for some of them. I will give my all, as I always have done, and I'm thoroughly excited about being back."
Blackpool are also reportedly closing in on a deal to sign Costa Rica international midfielder Jose Cubero, who made four substitute appearances in the World Cup, from Herediano.