Hi,
To get all the History does somewhat depend on where you were storing them before and how you moved stuff from one computer to another.
Open a Finder Window.
Go to your Home Folder - the one with the Little House icon.
Go to the Edit Menu and choose Show View Options.
In the panel that appears select the Show Library option.
In the Finder Window the Library should now appear along with Movies, Pictures, Sites and so on.
Now go to Messages inside the Library folder.
In here should be at least 4 items.
The Attachments Folder.
and three chat.db database items with slightly different names.
These three databases are where the previous history is store of iMessages if you never used the Save on Close option before iCloud Syncing was an option.
Save on Close items were saved in ~/Library/Containers/com.apple.iChat/Data/Library/Messages
(That ~/Library is short for the Hard Drive Name/Users/YourAccountHome Folder/Library)
You can click through the folders to get there or Copy the path I posted and paste it in to the Dialogue box you find in using the Go Menu > Go to Folder from any Finder Window.
The Messages folder has the Archive Folder in it and the Alias that points to the earlier Messages folder with the database item.
The Archive has all the saved chat that might include earlier AIM and Jabber and even Bonjour chats you may have had in previous OS versions of Messages.
Both these folders (~/Library/Messages and the .../Containers... one) can be copied to the new Mac if you Migrate the Mac User Account. This method should resolve any issues about Ownership and Read and Write permissions to the files that have been moved.
If you dragged the files from the old location to the new computer then the Ownership and Permissions may need to be sorted out.
See this Apple Document for that Resolve issues caused by changing the permissions of items in your home folder - Apple Support
Once you have done that then the iCloud syncing should bring you up to date with your other devices.
7:59 pm Thursday; November 15, 2018
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
MacBookPro 15" 2016 (High Sierra 10.13.x)
Mac OS X (10.6.8),
iPhone 6 iOS 11.x and an iPad (2)
