Between free-agent signings and players from the system added to the Cubs' 40-man roster, there are 13 new players on the 40-man since the 2015 season ended (not counting Trevor Cahill, who was re-signed as a free agent).
Here's the entire 40-man roster and how each player was acquired, sorted by type of signing, then by the date the player was acquired or selected.
Matt Szczur: Drafted in the 5th round June 8, 2010 Eric Jokisch: Drafted in the 11th round, June 8, 2010 Dallas Beeler: Drafted in the 41st round, June 9, 2010 Javier Baez: Drafted in the 1st round (9th overall pick) June 6, 2011 Dan Vogelbach: Drafted in the 2nd round June 6, 2011 Pierce Johnson: Drafted in the 1st round (43rd overall pick) June 4, 2012 Kris Bryant: Drafted in the 1st round (2nd overall pick) June 6, 2013 Kyle Schwarber: Drafted in the 1st round (4th overall pick) June 5, 2014
Zac Rosscup: Acquired by trade January 8, 2011 Travis Wood: Acquired by trade December 23, 2011 Anthony Rizzo: Acquired by trade January 6, 2012 Kyle Hendricks: Acquired by trade July 31, 2012 Christian Villanueva: Acquired by trade July 31, 2012 Jake Arrieta: Acquired by trade July 2, 2013 Pedro Strop: Acquired by trade July 2, 2013 Justin Grimm: Acquired by trade July 22, 2013 Neil Ramirez: Acquired by trade July 22, 2013 Carl Edwards Jr.: Acquired by trade July 22, 2013 Addison Russell: Acquired by trade July 5, 2014 Tommy La Stella: Acquired by trade November 16, 2014 Miguel Montero: Acquired by trade December 9, 2014 Spencer Patton: Acquired by trade November 20, 2015 Rex Brothers: Acquired by trade November 25, 2015 Adam Warren: Acquired by trade December 8, 2015
Free agency (9)
Chris Coghlan: Signed as a free agent January 20, 2014 Jason Hammel: Signed as a free agent December 12, 2014 Jon Lester: Signed as a free agent December 15, 2014 David Ross: Signed as a free agent December 23, 2014 Andury Acevedo: Signed as a free agent November 18, 2015 John Lackey: Signed as a free agent December 8, 2015 Ben Zobrist: Signed as a free agent December 8, 2015 Trevor Cahill: Signed as a free agent December 14, 2015 Jason Heyward: Signed as a free agent December 15, 2015
Arismendy Alcantara: Signed as an amateur international free agent November 3, 2008 Willson Contreras: Signed as an amateur international free agent July 15, 2009 Jeimer Candelario: Signed as an amateur international free agent November 20, 2010 Jorge Soler: Signed as an amateur international free agent June 30, 2012 Hector Rondon: Selected in the Rule 5 draft December 6, 2012 Clayton Richard: Acquired in a cash transaction July 3, 2015 Edgar Olmos: Claimed on waivers December 23, 2015
As you can see, the most frequent -- by far -- method of placing players on the current 40-man roster is by trade. Just one of those traded-for players (Rosscup) was acquired by the Jim Hendry regime, acquired along with Matt Garza (that trade, in which Chris Archer was sent to the Rays, was a bad deal from the Cubs' standpoint, but at least one player remains). Eight other players (Szczur, Jokisch, Beeler, Baez, Vogelbach, Alcantara, Contreras and Candelario) remain from the pre-Theo Epstein era.
Four of the seven 40-man players acquired via the draft are first-round picks; Beeler, by far, is the lowest-round choice (there isn't even a 41st round anymore).
Theo & Co. have been active in free agency both in big names (Lester, Heyward) and lesser-publicized acquisitions (Coghlan, Cahill).
Thought you would all enjoy this look at how the 2016 Cubs, at this writing, were put together.