Under the terms of the deal, CGX shareholders will receive $3.44 cash plus 1.651 RRD shares for each share in CGX, equivalent to a cash offer of $62 per share based on RRD's closing share price on 23 October.
RRD said this represented a total transaction value of approximately $620m, in addition to which it will assume Consolidated Graphics' net debt of $112m.
The deal, which has the unanimous agreement of both boards, is expected to close in Q1 2014, subject to the approval of CGX shareholders and the regulators.
CGX chairman and chief executive Joe Davis has signed a voting agreement pledging his shareholding, representing approximately 16.5% of CGX outstanding shares, in favour of the merger.
CGX reported revenues of $1bn in its results for the year ended 31 March 2013 and an EBITDA of $110m, meaning RRD's offer (including assumption of net debt) equates to 6.6x EBITDA.
One senior print executive remarked that this was "very good for a manufacturing business" adding "clearly, RRD wants to own as much market share as possible and likes CGX’s extensive digital offering – so it’s paying a premium".
RRD recorded net sales of $10.2bn for the 12 months to 31 December 2012 and an adjusted non-GAAP EBITDA of $1.2bn.
RR Donnelley's president and chief executive officer Thomas Quinlan III said: "Consolidated Graphics is an exceptional fit with RR Donnelley and we are delighted to welcome them to our organization.
"This strategic combination will complement the RR Donnelley platform and further enhance our ability to provide integrated communications solutions for our valued clients across all industry verticals."
Davis said: "Consolidated Graphics' success is due to our outstanding employees and their ability to provide the service and responsiveness of a local printing company while offering customers the flexible solutions and competitive pricing available from our wide network.
"Our customers will benefit significantly from RR Donnelley's broad range of printing capabilities and our combined geographic footprint. RR Donnelley's customers will benefit from the planned adoption of Consolidated Graphics' local service model for all of its commercial printing group."
Consolidated Graphics claims a world-leading position in digital printing, and is HP's biggest customer. It runs more than 220 high-end digital presses.
It has operations across the USA, a site in Japan, and has a European presence in the Czech Republic.
Consolidated Graphics' share price was at $63.60 at the time of writing.