When you add a user / group in SharePoint, you should see "Send an email invitation" check box to control whether or not send the welcome e-mail to the new users.
You could clear that check box and it should fix your problem.
Also, there are some situations when "Send an email invitation" is hidden.
I checked dialog's code-behind by reflector and find that:
Part of InitPage method of AclInv.cs:
this.PanelSendEmail.Visible = true;
this.PanelEmailBody.Visible = true;
this.txtEmailSubject.Text = SPResource.GetString(CultureInfo.CurrentCulture, "ACLInviteDefaultSubject", (object) this.Web.CurrentUser.Name, (object) this.TargetObjectTitle);
this.PanelRequireSignIn.Visible = true;
this.ifsSendEmail.Visible = true;
As you can see sharepoint checks "isEmailServerSet" before setting visibility to inviation configuration panels.
As the result, you need to configure outgoing e-mail settings in CA (Central Administration -> System settings -> Configure outgoing e-mail settings) to make invitation configuration visible in "Share" dialog.